单位根处的某些单U_q(gl_n)-模的Krull-Schmidt分解（英文）

Krull-Schmidt decomposition of the tensor products of certain simple U_q(gI_n)-modules at a root of unity

设F是特征0的域,q∈F是个单位根.以F为基域、以q为量子参数,令s_q(n)为秩n的限制量子对称代数,∧_q(n)为秩n的量子外代数.据[6],S_q(n)与∧_q(n)的齐次分量都是单的U_q(gI_n)-模.本文将把S_q(n)的齐次分量与∧_q(n)的齐次分量的张量积分解成不可分解模的直和.

Assume （F） to be a field of characteristic zero,and q ∈ （F） to be a root of unity.With （F） as the ground field and q as the quantum parameter,let sq（n） be the restricted quantum symmetric algebra of rank n,and ∧q（n） be the quantum exterior algebra of rank n.By [6],the homogenous components of both Sq（n） and ∧q（n） are simple Uq（gIn）-modules.In this paper,we decompose the tensor product of any homogenous component of sq（n） with any homogenous component of ∧q（n） into direct sum of indecomposable modules.