Tensor Product of Crystal Bases¶forUq(??}(m,n))-Modules
- Cite this article as:
- Kang, SJ. & Kwon, JH. Commun. Math. Phys. (2001) 224: 705. doi:10.1007/PL00005591
In this paper, we give a combinatorial algorithm of decomposing the tensor product of Uq(??(m,n))-crystals. Using the insertion scheme for (m,n)-hook semistandard tableaux, we show that there exists a bijection between the set of Littlewood–Richardson tableaux and the set of genuine highest weight vectors in the tensor product of Uq(??(m,n))-crystals. Hence the connected components are parametrized by the Littlewood–Richardson tableaux.
Unable to display preview. Download preview PDF.