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arXiv · 1803.06463

Multiplication formulas and semisimplicity for q-Schur superalgebras

Jie Du·Haixia Gu·Zhongguo Zhou
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Abstract

We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for q-Schur superalgebras. This gives a combinatorialisation of the relative norm approach developed by the first two authors. We then give several applications of the multiplication formulas, including the matrix representation of the regular representation and a semisimplicity criterion for q-Schur superalgebras. We also construct infinitesimal and little q-Schur superalgebras directly from the multiplication formulas and develop their semisimplicity criteria.

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BibTeXRIS

Jie Du, Haixia Gu, Zhongguo Zhou. 2018-03-17. Multiplication formulas and semisimplicity for q-Schur superalgebras. https://arxiv.org/abs/1803.06463

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