Gelfand--Kirillov dimensions of highest weight modules for basic classical Lie superalgebras

[2606.11551] Gelfand--Kirillov dimensions of highest weight modules for basic classical Lie superalgebras Skip to main content Search Submit Donate Log in Mathematics > Representation Theory arXiv:2606.11551 (math) [Submitted on 10 Jun 2026 ( v1 ), last revised 13 Oct 2026 (this version, v4)] Title: Gelfand--Kirillov dimensions of highest weight modules for basic classical Lie superalgebras Authors: Jing Jiang View PDF HTML (experimental) Abstract: We give exact Gelfand--Kirillov (GK) dimension formulas for simple highest weight modules of the basic classical Lie superalgebras considered in this paper. For the type II orthosymplectic algebras $D(m,n)$ and $B(m,n)$, we identify the PBW associated variety as a product of factor supports evaluated at highest weights for two compatible Borel subalgebras. This gives algorithms for arbitrary complex highest weights, without integrality or typicality hypotheses. In type $B$, the terminal factor is $\mathfrak{osp}(1|2n)$, for which we derive an insertion formula that distinguishes integer and half-integer shifted coordinates. For $G(3)$, $F(4)$ and $D(2,1;\alpha)$, finite odd-reflection procedures give exact formulas, their GK spectra, and finite-dimensionality criteria; we also describe the dependence on $\alpha$ in the last case. In type I, the GK dimension equals that of the simple even highest weight module for the distinguished Borel. The computations use the established ordinary Lie algebra formulas involving Lusztig's $\mathbf a$-function and Robinson--Schensted insertion. Comments: 50 pages Subjects: Representation Theory (math.RT) MSC classes: 17A70, 17B10, 17B20 Cite as: arXiv:2606.11551 [math.RT] (or arXiv:2606.11551v4 [math.RT] for this version) https://doi.org/10.48550/arXiv.2606.11551 Focus to learn more arXiv-issued DOI via DataCite 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) [v3] Sat, 22 Aug 2026 06:55:41 UTC (58 KB) [v4] Tue, 13 Oct 2026 09:34:32 UTC (69 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.RT < prev | next > new | recent | 2026-06 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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