| FullText URL | mjou_064_215_225.pdf |
|---|---|
| Author | Hyodo, Fumitake| |
| Abstract | This paper focuses on the theory of the Hecke rings associated with the general linear groups originally studied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings associated with the automorphism groups of certain algebras. Then, in the case of the Heisenberg Lie algebra, we show an analog of the classical theory. |
| Keywords | Hecke rings noncommutative rings |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 215 |
| End Page | 225 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_191_213.pdf |
|---|---|
| Author | Suzuki, Takeshi| Toyosawa, Yoshitaka| |
| Abstract | We present a conjectural hook formula concerning the number of the standard tableaux on "cylindric" skew diagrams. Our formula can be seen as an extension of Naruse's hook formula for skew diagrams. Moreover, we prove our conjecture in some special cases. |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 191 |
| End Page | 213 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_187_190.pdf |
|---|---|
| Author | Puthenpurakal, Tony J. | |
| Abstract | Let K be a field and consider the standard grading on A = K[X1, ... ,Xd]. Let I, J be monomial ideals in A. Let In(J) = (In : J∞) be the nth symbolic power of I with respect to J. It is easy to see that the function fI J (n) = e0(In(J)/In) is of quasi-polynomial type, say of period g and degree c. For n ≫ 0 say fIJ (n) = ac(n)nc + ac−1(n)nc−1 + lower terms, where for i = 0, ... , c, ai : N → Q are periodic functions of period g and ac ≠0. In [4, 2.4] we (together with Herzog and Verma) proved that dim In(J)/In is constant for n ≫ 0 and ac(−) is a constant. In this paper we prove that if I is generated by some elements of the same degree and height I ≥ 2 then ac−1(−) is also a constant. |
| Keywords | quasi-polynomials monomial ideals symbolic powers |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 187 |
| End Page | 190 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_153_186.pdf |
|---|---|
| Author | Nishiyama, Yuta| |
| Abstract | In this article, we introduce some identities obtained from the inner products of some symmetric polynomials including the Macdonald polynomials. These identities are obtained not only from the inner products, but also by constructing certain bijections. The bijections are constructed through transforming the Young diagrams of partitions. |
| Keywords | Macdonald polynomials Young diagram bijective proof |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 153 |
| End Page | 186 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_143_151.pdf |
|---|---|
| Author | Aokage, Kazuya | Tabata, Sumitaka | Yamada, Hiro-Fumi| |
| Abstract | A quantum version of classical Sylvester-Franke theorem is presented. After reviewing some representation theory of the quantum group GLq (n, C), the commutation relations of the matrix elements are verified. Once quantum determinant of the representation matrix is defined, the theorem follows naturally |
| Keywords | Quantum general linear group Sylvester-Franke theorem |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 143 |
| End Page | 151 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_117_141.pdf |
|---|---|
| Author | Wang, Qi| |
| Abstract | As the first attempt to classify τ-tilting finite two-point algebras, we have determined the τ-tilting finiteness for minimal wild two-point algebras and some tame two-point algebras. |
| Keywords | Support τ-tilting modules τ-tilting finite two-point algebras |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 117 |
| End Page | 141 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_109_116.pdf |
|---|---|
| Author | Yagita, Nobuaki| |
| Abstract | Let p be a prime number. For a given finite group G, let gr*γ(BG) be the associated ring of the gamma filtration of the topological K-theory for the classifying space BG. In this paper, we study gr*γ(BG) when G are abelian p-groups which are not elementary. In particular, we extend related Chetard’s results for such 2-groups to p-groups for odd p. |
| Keywords | K-theory gamma fitration abelian p-group |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 109 |
| End Page | 116 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_075_107.pdf |
|---|---|
| Author | Nagamachi, Ippei| |
| Abstract | We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under some assumptions. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa. |
| Keywords | good reduction, hyperbolic curve, polyucurve, ètale fundamental group. |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 75 |
| End Page | 107 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_063_073.pdf |
|---|---|
| Author | Tasaka, Koji| |
| Abstract | A partial answer to a conjecture about the rank of the matrix CN,r introduced by Francis Brown in the study of totally odd multiple zeta values is given. |
| Keywords | Multiple zeta values Period polynomials |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 63 |
| End Page | 73 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_047_061.pdf |
|---|---|
| Author | Yamanaka, Satoshi| |
| Abstract | The notion of weakly separable extensions was introduced by N. Hamaguchi and A. Nakajima as a generalization of separable extensions. The purpose of this article is to give a characterization of weakly separable polynomials in skew polynomial rings. Moreover, we shall show the relation between separability and weak separability in skew polynomial rings of derivation type. |
| Keywords | separable extension weakly separable extension skew polynomial ring derivation |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 47 |
| End Page | 61 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_031_045.pdf |
|---|---|
| Author | Yamagishi, Hiroyuki| |
| Abstract | We have the best constants of three kinds of discrete Sobolev inequalities on the complete bipartite graph with 2N vertices, that is, KN,N. We introduce a discrete Laplacian A on KN,N. A is a 2N ×2N real symmetric positive-semidefinite matrix whose eigenvector corresponding to zero eigenvalue is 1 = t(1, 1, … , 1)∈ C2N. A discrete heat kernel, a Green’s matrix and a pseudo Green’s matrix play important roles in giving the best constants. |
| Keywords | Discrete Sobolev inequality Discrete Laplacian Green’s matrix Reproducing relation |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 31 |
| End Page | 45 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_013_029.pdf |
|---|---|
| Author | Seita, Kohei| |
| Abstract | Let G be a finite group. In 1970s, T. Petrie defined the Smith equivalence of real G-modules. The Smith set of G is the subset of the real representation ring consisting of elements obtained as differences of Smith equivalent real G-modules. Various results of the topic have been obtained. The d-Smith set of G is the set of all elements [V ]−[W] in the Smith set of G such that the H-fixed point sets of V and W have the same dimension for all subgroups H of G. The results of the Smith sets of the alternating groups and the symmetric groups are obtained by E. Laitinen, K. Pawa lowski and R. Solomon. In this paper, we give the calculation results of the d-Smith sets of the alternating groups and the symmetric groups. In addition, we give the calculation results of the d-Smith sets of Cartesian products of the alternating groups and finite elementary abelian 2-groups. |
| Keywords | Real G-module Smith equivalence Oliver group alternating group |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 13 |
| End Page | 29 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_064_001_011.pdf |
|---|---|
| Author | Hoshi, Yuichiro| |
| Abstract | In the present paper, we consider torsion points on ample divisors on abelian varieties. We prove that, for each integer n ≤ 2, an effective divisor of level n on an abelian variety does not contain the subgroup of n-torsion points. Moreover, we also discuss an application of this result to the study of the p-rank of cyclic coverings of curves in positive characteristic. |
| Keywords | abelian variety torsion point curve p-rank |
| Published Date | 2022-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume64 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 1 |
| End Page | 11 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_008_189_194.pdf |
|---|---|
| Author | Nagahara, Takasi| Nobusawa, Nobuo| Tominaga, Hisao| |
| Published Date | 1958-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume8 |
| Issue | issue2 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 189 |
| End Page | 194 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©1958 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_008_181_188.pdf |
|---|---|
| Author | Nagahara, Takashi| |
| Published Date | 1958-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume8 |
| Issue | issue2 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 181 |
| End Page | 188 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©1958 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_008_143_179.pdf |
|---|---|
| Author | Otsuki, Tominosuke| |
| Published Date | 1958-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume8 |
| Issue | issue2 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 143 |
| End Page | 179 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©1958 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_008_133_142.pdf |
|---|---|
| Author | Nagahara, Takasi| Onodera, Takesi| Tominaga, Hisao| |
| Published Date | 1958-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume8 |
| Issue | issue2 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 133 |
| End Page | 142 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©1958 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_008_125_131.pdf |
|---|---|
| Author | Sugawara, Masahiro| |
| Published Date | 1958-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume8 |
| Issue | issue2 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 125 |
| End Page | 131 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©1958 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_008_117_123.pdf |
|---|---|
| Author | Tominaga, Hisao| |
| Published Date | 1958-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume8 |
| Issue | issue2 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 117 |
| End Page | 123 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©1958 by the Editorial Board of Mathematical Journal of Okayama University |
| FullText URL | mjou_008_107_116.pdf |
|---|---|
| Author | Ōtsuki, Tominosuke| |
| Published Date | 1958-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume8 |
| Issue | issue2 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 107 |
| End Page | 116 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©1958 by the Editorial Board of Mathematical Journal of Okayama University |
