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Zhanqiang Bai, Markus Hunziker, Xun Xie, Roger Zierau, On the Associated Variety of a Highest Weight Harish-Chandra Module, International Mathematics Research Notices, Volume 2025, Issue 8, April 2025, rnaf095, https://doi.org/10.1093/imrn/rnaf095
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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.
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