Slim cyclotomic q-Schur 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2018
- DOI:
- 10.48550/arXiv.1803.09185
- arXiv:
- arXiv:1803.09185
- Bibcode:
- 2018arXiv180309185D
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Quantum Algebra;
- Mathematics - Rings and Algebras