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arXiv · 1803.09185

Slim cyclotomic q-Schur algebras

Bangming Deng·Jie Du·Guiyu Yang
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Abstract

We construct a new basis for a slim cyclotomic $q$-Schur algebra $\cysSr$ via symmetric polynomials in Jucys--Murphy operators of the cyclotomic Hecke algebra $\cysHr$. We show that this basis, labelled by matrices, is not the double coset basis when $\cysHr$ is the Hecke algebra of a Coxeter group, but coincides with the double coset basis for the corresponding group algebra, the Hecke algebra at $q=1$. As further applications, we then discuss the cyclotomic Schur--Weyl duality at the integral level. This also includes a category equivalence and a classification of simple objects.

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BibTeXRIS

Bangming Deng, Jie Du, Guiyu Yang. 2018-03-25. Slim cyclotomic q-Schur algebras. https://arxiv.org/abs/1803.09185

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