2002 Fiscal Year Final Research Report Summary
Representation theory of Lie algebras and quantum groups
| Project/Area Number |
13440010
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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 | Osaka City University (2002)
Hiroshima University (2001) |
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Principal Investigator |
TANISAKI Toshiyuki Graduate school of Science, Professor, 大学院・理学研究科, 教授 (70142916)
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| Co-Investigator(Kenkyū-buntansha) |
KAWANAKA Noriaki Osaka Univ., Graduate school of Information Sience and technology, professor, 大学院・情報科学研究科, 教授 (10028219)
SHOJI Toshiaki Tokyo Science Univ., Faculty of science and tecnology, professor, 理工学部, 教授 (40120191)
KASHIWARA Masaki Kyoto Univ., Reseach Trstitute of Mathematical Science, professor, 数理解析研究所, 教授 (60027381)
KANEDA Masaharu Graduate school of Science, Professor, 大学院・理学研究科, 教授 (60204575)
SAITO Yoshihisa Univ. of Tokyo Graduate school of Mathematical Science, assistant professor, 大学院・数理化学研究科, 助教授 (20294522)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Infimte dimensiand Lie Igobras / quantum groups / algobrarc groups / Highestweight modulas |
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| Research Abstract |
1. Flag manifolds for quantum groups Tanisaki investigaled represecrtation theory of quantum groups using the flag manifolds of quanlum groups as non-commutative schemes. Especially, he has considered about the D-modyle theory and established a version of Beillnson-Bernstein correspondence proving a part of the conjecture by Lunts-Roscnberg
2. Finite dimensional representations of quantum sffine algebras Kashiwara investigated the crystal bases and gave a condition for the tensor product of fundamental modules to be irreducible. Nakajima indroduced a crystal structure on the set of certain monomials and gave a new proof for the fact that the standard modulesare tensor product of fundamental modulcs. He also gave a proof of Lusztig's conjecture about the cell structure of quantum affine algebras
3. Green functions assoclated to complex refiection groups Shoji constructed a new type of Macdonald polynomials as a two parameter version of Hall-Littlewood polynomial associated to complex refection groups
4. Characters of finite Chevalley groups Shoji investigated about the delermination of some scalars which are the remaining part in Lusztig's program determining the characters, and has decided them for the special lincar groups
5. Elliptic Lic algebras and assclated Artin groups and Hecke algebras Saito constructed a representation of exccptional elliptic Lie algebsa using the method of vertex operator algebras and computed its characters. He also get a result about a relation between the elilptic Hecke algebras and the double affino Hecke algebras
Sphcrical homogeneous spaces over p-adic flekis Kato gave a dimension formula for spherical functions for some cases and constructed a general theory of spherical functions for symmetric spaces
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