[Submitted on 10 Jun 2026 (v1), last revised 16 Jun 2026 (this version, v2)]

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Abstract:In this paper we develop a combinatorial algorithm to compute the Gelfand--Kirillov (GK) dimension of simple highest weight modules for basic classical Lie superalgebras. Building upon the results for classical Lie algebras via Lusztig's {\bf a}-function and the Robinson--Schensted (RS) insertion algorithm, we extend these techniques to the super setting, providing explicit formulas for types $\mathfrak{sl}(m|n)$ and $\mathfrak{osp}(2|2n)$. Our results show that the GK dimension of a simple highest weight module is determined entirely by the even part of the Lie superalgebras.

Submission history

From: Jing Jiang [view email]
[v1] Wed, 10 Jun 2026 01:21:50 UTC (45 KB)
[v2] Tue, 16 Jun 2026 07:41:34 UTC (46 KB)

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