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Slim cyclotomic q-Schur algebras
- Publication Year :
- 2018
-
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.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1803.09185
- Document Type :
- Working Paper