| 2011/1/17 | 16:30–17:30 |
| 登 録 ID | 1292983818-27 | |||
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| 種 別 | Seminar Representation Theory Seminar | |
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| 講 演 者 | Ian M. Musson (University of Wisconsin-Milwaukee) | |
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| タ イ ト ル | Combinatorics of Character Formulas for the Lie Superalgebra gl(m,n) | |
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| 会 場 | 409 in Bldg. Sci. 1 | |
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| 要 旨 | Let g be the Lie superalgebra gl(m,n). Algorithms for computing the composition factors and multiplicities of Kac modules for g were given by Vera Serganova and by Jon Brundan. We give a combinatorial proof of the equivalence between the two algorithms. The proof uses weight and cap diagrams introduced by J. Brundan and C. Stroppel, and cancelations between paths in a graph G defined using these diagrams. Each vertex of G corresponds to a highest weight of a finite dimensional simple module, and each edge is weighted by a nonnegative integer. If E is the subgraph of G obtained by deleting all edges of positive weight, then E is the graph that describes non-split extensions between simple highest weight modules. This talk is based on joint work with Vera Serganova of the University of California-Berkeley. | |||
| 責 任 者 | 宮地兵衛 |
| 登 録 ID | 1292983818-27 | |||
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| 種 別 | セミナー 表現論セミナー | |
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| 属 性 | |
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| 講 演 者 | Ian M. Musson (University of Wisconsin-Milwaukee) | |
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| タ イ ト ル | Combinatorics of Character Formulas for the Lie Superalgebra gl(m,n) | |
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| 会 場 | 理1号館 409講義室 | |
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| 要 旨 | Let g be the Lie superalgebra gl(m,n). Algorithms for computing the composition factors and multiplicities of Kac modules for g were given by Vera Serganova and by Jon Brundan. We give a combinatorial proof of the equivalence between the two algorithms. The proof uses weight and cap diagrams introduced by J. Brundan and C. Stroppel, and cancelations between paths in a graph G defined using these diagrams. Each vertex of G corresponds to a highest weight of a finite dimensional simple module, and each edge is weighted by a nonnegative integer. If E is the subgraph of G obtained by deleting all edges of positive weight, then E is the graph that describes non-split extensions between simple highest weight modules. This talk is based on joint work with Vera Serganova of the University of California-Berkeley. | |||
| 責 任 者 | 宮地兵衛 |