Quantum Schur algebras revisited |
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Authors: | Bangming Deng Guiyu Yang |
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Affiliation: | School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China |
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Abstract: | A geometric construction of quantum Schur algebras was given by Beilinson, Lusztig and MacPherson in terms of pairs of flags in a vector space. By viewing such pairs of flags as representations of a poset, we give a recursive formula for the structure constants of quantum Schur algebras which is related to certain Hall polynomials. As an application, we provide a direct proof of the fundamental multiplication formulas which play a key role in the Beilinson-Lusztig-MacPherson realization of quantum gln. In the appendix we show how to groupoidify quantum Schur algebras in the sense of Baez, Hoffnung and Walker. |
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Keywords: | 20G43 17B37 |
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