Frobenius map for the centers of Hecke algebras
Representation Theory
2015-06-08 v2 Combinatorics
Quantum Algebra
Abstract
We introduce a commutative associative graded algebra structure on the direct sum Z of the centers of the Hecke algebras associated to the symmetric groups in n letters for all n. As a natural deformation of the classical construction of Frobenius, we establish an algebra isomorphism from the algebra Z to the ring of symmetric functions. This isomorphism provides an identification between several distinguished bases for the centers (introduced by Geck-Rouquier, Jones, Lascoux) and explicit bases of symmetric functions.
Keywords
Cite
@article{arxiv.1208.4446,
title = {Frobenius map for the centers of Hecke algebras},
author = {Jinkui Wan and Weiqiang Wang},
journal= {arXiv preprint arXiv:1208.4446},
year = {2015}
}
Comments
15 pages, v2, updated introduction, mild corrections of typos, to appear in Transactions of the American Mathematical Society