On the Associated Variety of a Highest Weight Harish-Chandra Module

Zhanqiang Bai; Markus Hunziker; Xun Xie; Roger Zierau

doi:10.1093/imrn/rnaf095

On the Associated Variety of a Highest Weight Harish-Chandra Module

Zhanqiang Bai
, Markus Hunziker^*
, Xun Xie
, Roger Zierau

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a simple formula that calculates the associated variety of a highest weight Harish-Chandra module directly from its highest weight. We also give a formula for the Gelfand-Kirillov dimension of a highest weight Harish-Chandra module, which is uniform across Cartan types and is valid for arbitrary infinitesimal character.

Original language	English
Article number	rnaf095
Journal	International Mathematics Research Notices
Volume	2025
Issue number	8
DOIs	https://doi.org/10.1093/imrn/rnaf095
Publication status	Published - 1 Apr 2025
Externally published	Yes

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10.1093/imrn/rnaf095

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AB - We prove a simple formula that calculates the associated variety of a highest weight Harish-Chandra module directly from its highest weight. We also give a formula for the Gelfand-Kirillov dimension of a highest weight Harish-Chandra module, which is uniform across Cartan types and is valid for arbitrary infinitesimal character.

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On the Associated Variety of a Highest Weight Harish-Chandra Module

Abstract

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