2003 Fiscal Year Final Research Report Summary
Representation theory of algebraic groups, Hecke algebras and complex reflection groups
| Project/Area Number |
13440014
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nagoya University (2003)
Tokyo University of Science (2001-2002) |
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Principal Investigator |
SHOJI Toshiaki Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (40120191)
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| Co-Investigator(Kenkyū-buntansha) |
ARAKI Susumu Kyoto University, RIMS, Associate Professor, 大学院・数理解析研究所, 助教授 (40212641)
SHINODA Ken-ichi Sophia University, Faculty of Science and Technology, Professor, 理工学部, 教授 (20053712)
KAWANAKA Noriaki Osaka University, Graduate School of Information, Professor, 大学院・情報科学研究科, 教授 (10028219)
UZAWA Tohru Nagoya University, Graduate School of Math., Professor, 大学院・多元数理科学研究科, 教授 (40232813)
GYOJA Akihiko Nagoya University, Graduate School of Math., Professor, 大学院・多元数理科学研究科, 教授 (50116026)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Luszfig's conjecture / special linear group / irreducible character / almost character / character sheaf / Shintani descent / symmetric space |
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| Research Abstract |
(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.
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