A_n型量子群的基本模的典范基

Canonical Basis for Fundamental Modules of Quantized Enveloping Algebras of Type A_n

设g是An型的有限维复单李代数,U是g的量子群.对g的每一个支配权λ,存在一个最高权λ的有限维不可约最高权U-模V(λ).本文确定n≤5时An型量子群的基本模V(λ)(即λ是基本支配权)的典范基.

Let g be a finite-dimensional complex simple Lie algebra of type An ,and U be the quantumgroup of g- For each dominant weight A in the weight lattice of g there is an irreducible, finite-dimensional highest weight Umodule V（ λ ） with highest weight λ. Canonical basis for fundamental modules of quantum group of type An when n≤5 are determined in this paper.