Representation theory of algebraic groups, Hecke algebras and complex reflection groups

代数群的表示论、赫克代数和复反射群

• 批准号: 13440014
• 负责人: SHOJI Toshiaki
• 金额: $ 5.31万
• 依托单位: Nagoya University (2003)Tokyo University of Science (2001-2002)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440014/
• 关键词: Luszfig's conjecture; special linear group; irreducible character; almost character; character sheaf; Shintani descent; symmetric space; 代数群; Green関数; Hall-Littlewood関数; Macdonald関数; 複素鏡映群; 一般Green関数; graded Hecke algebra; ヘッケ環; 表現論; Ariki

(1) I have proved the Luszfig's conjecture concerning the characters of finite special linear group SLn(〓_q) over finite field 〓_q. This conjecture provides as a general algorithm of computing irreducible characters of reductive group G(〓_q) over finite field, which is stated as 「almost characters and characteristic functions of character sheaves coincides with up to scalar multiple」. This conjecture we proved by the head investigator in the case where the center of G is connected. SLn is an example of disconnected enter. We can determine the scalars also, and we obtain a complete algorithm of computing irreducible characters.(2) By the joint work with K.Sorlin, I have determined the deconpositon of the presentation G(〓_q^2) -with G(〓_q^2)/G(〓_q) for G=SLn.

（1）我提供了有关有限的线性组SLN（〓_Q）的字符的luszfig的概念。该概念提供了计算有限字段的减少G组（〓_Q）的不可减少字符的一般算法，该字段被称为“字符滑轮的几乎字符和字符函数与标量倍数重合相吻合”。在连接G的中心的情况下，首席调查员提供了这个概念。 SLN是断开Enter的示例。我们也可以确定标量，并获得计算不可约特征的完整算法。（2）通过与K.Sorlin的联合工作，我确定了g（〓_q^2）-with g（〓_q^2）/g（〓_q）的介绍g（〓_q^2）的deconpositon。

项目成果

Susumu Ariki: "Uno's conjecture on representation types of Hecke algbra"Algebraic Combinatorics and Quantum groups. 1-9 (2003)

Susumu Ariki：“Uno 关于 Hecke 代数表示类型的猜想”代数组合和量子群。

Susumu Ariki: "Representations of Quantum algebras and combinatorics of Young tableaux"AMS, University lecture series. 155 (2002)

Susumu Ariki：“Young tableaux 的量子代数和组合学的表示”AMS，大学讲座系列。

Kiyotaka Ohkura: "On certain bases for Ariki-Koike algebras arising from canonical bases for U_v(sl_m)"SUT J. of Mathematics. 38. 145-173 (2002)

Kiyotaka Ohkura：“关于由 U_v(sl_m) 规范基产生的 Ariki-Koike 代数的某些基”SUT J. of Mathematics。

T.Shoji: "Green functions attached to limit symbols"Adv.Studies in Pure Math.. (発表予定).

T.Shoji：“附加到极限符号的绿色函数”Adv.Studies in Pure Math..（待提交）。

T.Shoji: "On Green functions associated to Complex reflection groups"Sugaku Exposition. (発表予定).

T.Shoji：“论与复杂反射群相关的绿色函数”Sugaku Exposition（待提交）。