Graded $q$-Schur algebras
Abstract
Generalizing recent work of Brundan and Kleshchev, we introduce grading on Dipper-James' $q$-Schur algebra, and prove a graded analogue of the Leclerc and Thibon's conjecture on the decomposition numbers of the $q$-Schur algebra when $q^2\neq1$ and $q^3\neq1$.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2009
- DOI:
- 10.48550/arXiv.0903.3453
- arXiv:
- arXiv:0903.3453
- Bibcode:
- 2009arXiv0903.3453A
- Keywords:
-
- Mathematics - Representation Theory;
- Mathematics - Quantum Algebra;
- 17B37
- E-Print:
- 25 pages, (v2) added details of the proof, (v3) have changed notations to standard ones and corrected various confusions