Tensor products of infinite dimensional modules in the BGG category of a quantized simple Lie algebra of type ADE

Authors : Zhaoting Wei

Pages : 108-120

Doi:10.24330/ieja.1357059

View : 112 | Download : 50

Publication Date : 2024-01-09

Article Type : Research Paper

Abstract :We consider the BGG category $\\O$ of a quantized universal enveloping algebra $U_q(\\mathfrak{g})$. It is well-known that $M\\otimes N\\in \\O$ if $M$ or $N$ is finite dimensional. When $\\mathfrak{g}$ is simple and of type ADE, we prove in this paper that $M\\otimes N\\notin \\O$ if $M$ and $N$ are both infinite dimensional.
Keywords : BGG category, quantized universal enveloping algebra, tensor product, formal character

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