2001 Fiscal Year Final Research Report Summary
Representation theory and combinatorics of classical groups, quantum groups and Hecke algebras
| Project/Area Number |
12640011
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | The University of Tokyo |
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Principal Investigator |
TERADA Itaru University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (70180081)
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| Co-Investigator(Kenkyū-buntansha) |
OKADA Soichi Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (20224016)
TANAKA Yohei Tokyo University of Mercantile Marine, Department of Mathematics, Associate Professor, 商船学部, 助教授 (00135295)
KOIKE Kazuhiko Aoyama Gakuin University, Department of Mathematics, Professor, 理工学部, 教授 (70146306)
OCHIAI Hiroyuki Tokyo Institute of Technology, Department of Mathematics, Associate Professor, 大学院・理工学研究科, 助教授 (90214163)
KOBAYASHI Toshiyuki University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (80201490)
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| Project Period (FY) |
2000 – 2001
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| Keywords | combinatorics / representation theory / Young diagrams / the Robinson-Schensted correspondence / the Springer variety / partially ordered sets / involutions / Brauer diagrams |
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| Research Abstract |
Throughout the two years, we investigated the possibility of providing some combinatorial interpretation to the "generalized Robinson-Schensted correspondence for real Lie groups" in the case where the group is SU^*(2n), explicitly described by P. Trapa. This is a bijection between the so-called Brauer diagrams on 2n points (which can also be interpreted as the fixed-point-free involutions) and the standard Young tableaux with 2n boxes whose column lengths are all even. One possible approach is, utilizing the fact that the classical Robinson-Schensted correspondence gives a bijection between the same sets, to find a transformation on Brauer diagrams which, when composed with the classical Robinson-Schensted correspondence, gives Trapa's bijection. Another possible approach is to characterize Trapa's bijection using some combinatorial quantities, in the same sense that the classical Robinson-Schensted correspondence can be characterized by certain invariants of posets due to Greene and
… More
Kleitman. In the first year, we obtained a conjecture in the second direction. We are still in pursuit of this conjecture Through interaction with various researchers, both domestic and overseas, we have received several interesting suggestions. One is to look for further possibility of extending our geometric interpretation to the Knuth version of the updown Robinson-Schensted correspondence devised by Pak and Postnikov. There has been another suggestion, somewhat related, that the irreducible decomposition of the variety of N-stable flags with gaps in dimensions is not yet clear. In view of these suggestions, it looks also necessary to find new approaches to combinatorial interpretations through generalization to the Knuth version, possibly as well as piecewise linear version. On the other hand, we continued to support T. Roby's research on constructing bijections giving the formal character identities corresponding to the decomposition of the tensor powers of the Weil representation of Sp(2n, R). This has come to a conclusion in the case n = 2. Less
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Research Products
(15 results)
