2013/03/25 by Xingyu Dai, Fang Li, Dai, Xingyu +3
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1303.6040
14 pages
arxiv created 2013/05/20 · arxiv updated 2013/05/21
In this paper, we construct the q-Schur modules as left principle ideals of the cyclotomic q-Schur algebras, and prove that they are isomorphic to those cell modules defined in \cite8 and \cite15 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 \cite23.