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Mathematics > Representation Theory

arXiv:1810.06980 (math)
[Submitted on 16 Oct 2018 (v1), last revised 16 Nov 2020 (this version, v3)]

Title:On BBW parabolics for simple classical Lie superalgebras

Authors:Dimitar Grantcharov, Nikolay Grantcharov, Daniel K. Nakano, Jerry Wu
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Abstract:In this paper the authors introduce a class of parabolic subalgebras for classical simple Lie superalgebras associated to the detecting subalgebras introduced by Boe, Kujawa and Nakano. These parabolic subalgebras are shown to have good cohomological properties governed by the Bott-Borel-Weil theorem involving the zero component of the Lie superalgebra in conjunction with the odd roots. These results are later used to verify an open conjecture given by Boe, Kujawa and Nakano pertaining to the equality of various support varieties.
Subjects: Representation Theory (math.RT)
MSC classes: 17B20, 17B56
Cite as: arXiv:1810.06980 [math.RT]
  (or arXiv:1810.06980v3 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1810.06980

Submission history

From: Daniel Nakano [view email]
[v1] Tue, 16 Oct 2018 13:28:32 UTC (31 KB)
[v2] Fri, 22 Mar 2019 09:40:34 UTC (32 KB)
[v3] Mon, 16 Nov 2020 02:31:31 UTC (36 KB)
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