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Evaluation maps for affine quantum Schur algebras.
- Source :
-
Journal of Algebra . Jul2024, Vol. 650, p23-53. 31p. - Publication Year :
- 2024
-
Abstract
- For a ∈ C ⁎ there are two natural evaluation maps ev a and ev a from the affine Hecke algebra H ▵ (r) C to the Hecke algebra H (r) C. The maps ev a and ev a induce evaluation maps ev ˜ a and ev ˜ a from the affine quantum Schur algebra S ▵ (n , r) C to the quantum Schur algebra S (n , r) C , respectively. In this paper we prove that the evaluation map ev ˜ a (resp. ev ˜ a) is compatible with the evaluation map Ev a (resp. Ev (− 1) n a q n ) for quantum affine sl n. Furthermore we compute the Drinfeld polynomials associated with the simple S ▵ (n , r) C -modules which come from the simple S (n , r) C -modules via the evaluation maps ev ˜ a. Then we characterize finite-dimensional irreducible S ▵ (n , r) C -modules which are irreducible as S (n , r) C -modules for n > r. As an application, we characterize finite-dimensional irreducible modules for the affine Hecke algebra H ▵ (r) C which are irreducible as modules for the Hecke algebra H (r) C. [ABSTRACT FROM AUTHOR]
- Subjects :
- *AFFINE algebraic groups
*HECKE algebras
*MODULES (Algebra)
*ALGEBRA
*POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 650
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 177109996
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2024.03.020