Multiplication formulas and semisimplicity for q-Schur superalgebras
Multiplication formulas and semisimplicity for q-Schur superalgebras
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DOI：
10.1017/nmj.2018.12
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Zhongguo Zhou
中科院分区：
文献类型：
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作者：
Jie Du;Haixia Gu;Zhongguo Zhou
We investigate products of certain double cosets for the symmetric.group and use the findings to derive some multiplication formulas for the qSchur superalgebras. This gives a combinatorialization of the relative norm.approach developed in Du and Gu (A realization of the quantum supergroup.U(glm|n), J. Algebra 404 (2014), 60–99). 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.
