| 2010/12/22 | 16:30–17:30 |
| 登 録 ID | 1291890289-07 | |||
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| 種 別 | Seminar Representation Theory Seminar | |
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| 講 演 者 | John Enyang (The University of Melbourne) | |
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| タ イ ト ル | Jucys-Murphy elements and representations of partition algebras | |
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| 会 場 | 307 in Bldg. Sci. 1 | |
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| 要 旨 | Using a presentation for the partition algebras given by Halverson and Ram, we provide a recursive definition for a large family of commuting (Jucys–Murphy) elements in the partition algebras, and an integral Murphy-type basis for the partition algebras, with respect to which the commuting family acts triangularly. Schur–Weyl will show that this recursively defined commuting family of Jucys-Murphy elements coincides exactly with the family of commuting elements given diagrammatically by Halverson and Ram. Our presentation will conclude with a discussion of further applications of the Jucys–Murphy elements to the study of the representations of the partition algebras. | |||
| 責 任 者 | 宮地兵衛 |
| 登 録 ID | 1291890289-07 | |||
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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 | John Enyang (The University of Melbourne) | |
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| タ イ ト ル | Jucys-Murphy elements and representations of partition algebras | |
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| 日 時 |
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| 会 場 | 理1号館 307セミナー室 | |
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| 要 旨 | Using a presentation for the partition algebras given by Halverson and Ram, we provide a recursive definition for a large family of commuting (Jucys–Murphy) elements in the partition algebras, and an integral Murphy-type basis for the partition algebras, with respect to which the commuting family acts triangularly. Schur–Weyl will show that this recursively defined commuting family of Jucys-Murphy elements coincides exactly with the family of commuting elements given diagrammatically by Halverson and Ram. Our presentation will conclude with a discussion of further applications of the Jucys–Murphy elements to the study of the representations of the partition algebras. | |||
| 責 任 者 | 宮地兵衛 |