Representation theory of Iwahori-Hecke algebras and reflection groups
| Project/Area Number |
23540026
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Sophia University |
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Principal Investigator |
Gomi Yasushi 上智大学, 理工学部, 准教授 (50276515)
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| Co-Investigator(Kenkyū-buntansha) |
NAKASHIMA Toshiki 上智大学, 理工学部, 教授 (60243193)
SHINODA Ken-ichi 上智大学, 理工学部, 教授 (20053712)
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| Research Collaborator |
Ma. Louise Antonette N. De Las Penas Ateneo de Manila University
Loyola Mark L. Ateneo de Manila University
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 岩堀ヘッケ環 / マルコフトレース / 鏡映群 / ガウス和 / ストリングC群 |
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| Outline of Final Research Achievements |
I studied q-analogues of Gauss sums on finite Coxeter groups which are generalization of classical Gauss sums. Then I gave the definition of Gauss sums on the Iwahori-Hecke algebras of type A and determined the values. Furthermore, I found that the corresponding trace functions on Iwahori-Hecke algebras are closely related to the Markov trace, and determined the values of the trace functions.
In addition, I studied the classification of string C-groups which are generalization of Coxeter groups. I focused into 2-groups, and I proved that in case of rank 3, all string C-groups are obtained as central extensions of string C-groups by 2. Using this theorem, I determined all string C-groups of order 1024.
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Report
(6 results)
Research Products
(31 results)
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[Presentation] Polyhedral Realizations of Crystal Bases2015
Author(s)
T. Nakashima
Organizer
8th South Eastern Lie Theory Workshop on Algebraic and Combinatiroal Representaion Theory, Discussion Sessions
Place of Presentation
North Carolina State University (USA)
Year and Date
2015-10-10
Related Report
Int'l Joint Research / Invited
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