Author:
Chen Chih-Whi,Coulembier Kevin,Mazorchuk Volodymyr
Abstract
AbstractWe prove that the tensor product of a simple and a finite dimensional $${\mathfrak {sl}}_n$$
sl
n
-module has finite type socle. This is applied to reduce classification of simple $${\mathfrak {q}}(n)$$
q
(
n
)
-supermodules to that of simple $${\mathfrak {sl}}_n$$
sl
n
-modules. Rough structure of simple $${\mathfrak {q}}(n)$$
q
(
n
)
-supermodules, considered as $${\mathfrak {sl}}_n$$
sl
n
-modules, is described in terms of the combinatorics of category $${\mathcal {O}}$$
O
.
Publisher
Springer Science and Business Media LLC
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