1. Slim cyclotomic q-Schur algebras
- Author
-
Deng, Bangming, Du, Jie, and Yang, Guiyu
- Subjects
Mathematics - Representation Theory ,Mathematics - Quantum Algebra ,Mathematics - Rings and Algebras - 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.
- Published
- 2018