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

Year 2024, Volume: 35 Issue: 35, 108 - 120, 09.01.2024

Zhaoting Wei

https://doi.org/10.24330/ieja.1357059

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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