(13004)A Basis of the q-Schur Module

来源:数学科学研究中心

Abstract
In this paper, we construct the q-Schur modules as left principle ideals of the cyclotomicq-Schur algebras, and prove that  they are isomorphic to those cell modules defined in [3] and [10] at any level r. Then we prove that these q-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 [20].

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