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GU Hai-xia, WANG Jian-pan. Krull--Schmidt decomposition of the tensor products of certain simpleUq(gln)-modules at a root of unity[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 1-13.
Citation:
GU Hai-xia, WANG Jian-pan. Krull--Schmidt decomposition of the tensor products of certain simpleUq(gln)-modules at a root of unity[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 1-13.
GU Hai-xia, WANG Jian-pan. Krull--Schmidt decomposition of the tensor products of certain simpleUq(gln)-modules at a root of unity[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 1-13.
Citation:
GU Hai-xia, WANG Jian-pan. Krull--Schmidt decomposition of the tensor products of certain simpleUq(gln)-modules at a root of unity[J]. Journal of East China Normal University (Natural Sciences), 2013, (6): 1-13.
Assume $\mathscr{F}$ to be a field of characteristic zero,
and $q\in \mathscr{F}$ to be a root of unity. With $\mathscr F$ as
the ground field and $q$ as the quantum parameter, let
$\mathsf{s}_q(n)$ be the restricted quantum symmetric algebra of
rank $n$, and $\Wedge_q(n)$ be the quantum exterior algebra of rank
$n$. By [6], the homogenous components of both $\mathsf{s}_q(n)$ and
$\Wedge_q(n)$ are simple $U_q(\mathfrak{gl}_n)$-modules. In this
paper, we decompose the tensor product of any homogenous component
of $\mathsf{s}_q(n)$ with any homogenous component of $\Wedge_q(n)$
into direct sum of indecomposable modules.
{AW} ANDERSEN H H, WEN K X. Representations of quantum algebras, the mixed case [J]. Journal f\"ur die Reine und Angewandte Mathematik, 1992, 427: 35--50.
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