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On the annihilator variety of a highest weight Harish-Chandra module (2408.07951v1)
Published 15 Aug 2024 in math.RT and math.RA
Abstract: Let $G$ be a Hermitian type Lie group with maximal compact subgroup $K$. Let $L(\lambda)$ be a highest weight Harish-Chandra module of $G$ with the infinitesimal character $\lambda$. By using some combinatorial algorithm, we obtain a description of the annihilator variety of $L(\lambda)$. As an application, when $L(\lambda)$ is unitarizable, we prove that the Gelfand-Kirillov dimension of $L(\lambda)$ only depends on the value of $z=(\lambda,\beta{\vee})$, where $\beta$ is the highest root.