A Basis of the $q$-Schur Module
Representation Theory
2013-05-21 v2 Rings and Algebras
Abstract
In this paper, we construct the -Schur modules as left principle ideals of the cyclotomic -Schur algebras, and prove that they are isomorphic to those cell modules defined in \cite{8} and \cite{15} at any level . Then we prove that these -Schur modules are free modules and construct their bases. This result gives us new versions of several results about the standard basis and the branching theorem. With the help of such realizations and the new bases, we re-prove the Branch rule of Weyl modules which was first discovered and proved by Wada in \cite{23}.
Cite
@article{arxiv.1303.6040,
title = {A Basis of the $q$-Schur Module},
author = {Xingyu Dai and Fang Li and Kefeng Liu},
journal= {arXiv preprint arXiv:1303.6040},
year = {2013}
}
Comments
14 pages