Tensor Product of Crystal BasesforU_{q}(??}(m,n))Modules
Abstract
In this paper, we give a combinatorial algorithm of decomposing the tensor product of U_{q}(??(m,n))crystals. Using the insertion scheme for (m,n)hook semistandard tableaux, we show that there exists a bijection between the set of LittlewoodRichardson tableaux and the set of genuine highest weight vectors in the tensor product of U_{q}(??(m,n))crystals. Hence the connected components are parametrized by the LittlewoodRichardson tableaux.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2001
 DOI:
 10.1007/PL00005591
 Bibcode:
 2001CMaPh.224..705K