Multiplication formulas and semisimplicity for q-Schur superalgebras
Quantum Algebra
2018-03-20 v1 Group Theory
Rings and Algebras
Representation Theory
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.
Cite
@article{arxiv.1803.06463,
title = {Multiplication formulas and semisimplicity for q-Schur superalgebras},
author = {Jie Du and Haixia Gu and Zhongguo Zhou},
journal= {arXiv preprint arXiv:1803.06463},
year = {2018}
}
Comments
22 pages. Nagoya J. Math. (to appear)