RESEARCH ON THE MODULAR REPRESENTATIONS OF FINITE GROUPS

有限群模表示的研究

• 批准号: 09640056
• 负责人: TSUSHIMA Yukio
• 金额: $ 1.86万
• 依托单位: OSAKA CITY UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640056/
• 关键词: Broue conjecture; derived equivalence; perfect isometry; AR-sequence; Hecke algebra; symmetric group; groups of Lie type; D-module; 有限群; p-モジュラー系; 直交関係; ブロック直交関係; 互換; Robinson

(1) Indecomposable modules over finite groupsSome contributions to the solution of the Broue conjecture are made especially in linear groups and the Glauberman correspondence cases. The tree classes of some Auslander-Reiten components for integral group rings of non cyclic p-groups are determined.(2) Endomorphism rings of permutation modulesThe orthgonality relation of characters of blocks of finite groups is generalized to that of blocks of Hecke algebras in the case where the base subgroup under consideration has order prime to the characteristic of the base field.Some new results are obtained about the number of irreducible modular constituents of Specht modules of the symmetric group.(3) Representation theory of groups of Lie typeSome foundations on the theory of D-modules in positive characteristic are established. A new approach is made using Kashiwara's crystal basis to Mathieu's theorem concerning the tensor products of modules with good filtrations.

(1)有限群上的不可分解模对Broue猜想的解决作出了一些贡献，特别是在线性群和Glauberman对应的情况下。确定了非循环p-群的整群环的某些Auslander-Reiten分支的树类。(2)置换模的自同态环将有限群的块的特征标的正交关系推广到Hecke代数的块的正交关系，在所考虑的基子群的阶与基域的特征标互素的情况下，得到了关于对称群的Specht模的不可约模成分个数的一些新结果. (3)Lie型群的表示理论建立了正特征D-模理论的一些基础。本文利用Kashiwara的晶体基对Mathieu关于具有好滤子的模的张量积定理作了一个新的探讨。

项目成果

井上孝之: "On Auslander-Reiten components and triviol source modules for imtegral group ringo of p-groups" Journal of Algelra. 203. 374-384 (1998)

Takayuki Inoue：“关于 p 群的不整群环的 Auslander-Reiten 分量和琐碎源模块”《Algelra 杂志》203. 374-384 (1998)。

奥山哲郎: "Decompositiov numlers for Sp(4,g)" Journal of Algelra. 199. 544-555 (1998)

Tetsuro Okuyama：“Sp(4,g) 的分解数字”Algelra 杂志 199. 544-555 (1998)

M.Kaneda: "Some generalities on D-modules in positive characteristic" Pacific J.Math.183. 103-183 (1998)

M.Kaneda：“积极特征中 D 模块的一些概括”Pacific J.Math.183。

稗田吉成: "On S_R(H)-blocks for finite groups" Journal of Algebra. 202. 583-588 (1998)

Yoshinari Hieda：“关于有限群的 S_R(H) 块”代数杂志 202. 583-588 (1998)。

A.Watanabe: "The Glauberman character correspondence and perfect isometrie of finite groups" J.Alg. (in print).

A.Watanabe：“格劳伯曼字符对应和有限群的完美等距”J.Alg。