Let $A, B$ be finitely generated (noncommutative) algebras over a field $k$ (say, algebraically closed). Can we get all irreducible representations of $A \otimes_k B$ from tensoring representations of $A$ with representations of $B$? I'm especially interested in the case where $A, B$ are the enveloping algebras of finite-dimensional Lie algebras.
Irreducible representations of a tensor product
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0@Matt: Sure. (and extra characters) – 2012-04-13
1 Answers
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This is true for finite-dimensional representations, but false for infinite-dimensional ones. See pg. 31-32 of these lecture notes.
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0Very nice. Thanks. – 2012-04-12