Annihilation Theorem and Separation Theorem for basic classical Lie superalgebras

Gorelik, María

doi:10.1090/s0894-0347-01-00382-4

Cited by 26 publications

(18 citation statements)

References 23 publications

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“…We claim that span C {u k v : k ≥ 0} is finite dimensional. Theorem 2.5 in [15] (see also Lemma 8.3.1 in [7] for a correction of a misprint) implies that there exist z 0 , z 1 , . .…”

Section: Whittaker Modules For Basic Classical Lie Superalgebras Of T...mentioning

confidence: 99%

Whittaker Categories and Whittaker Modules for Lie Superalgebras

Bagci

Christodoulopoulou

Wiesner

2014

Communications in Algebra

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Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, a description of the strongly typical simple Whittaker modules.

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“…We claim that span C {u k v : k ≥ 0} is finite dimensional. Theorem 2.5 in [15] (see also Lemma 8.3.1 in [7] for a correction of a misprint) implies that there exist z 0 , z 1 , . .…”

Section: Whittaker Modules For Basic Classical Lie Superalgebras Of T...mentioning

confidence: 99%

Whittaker Categories and Whittaker Modules for Lie Superalgebras

Bagci

Christodoulopoulou

Wiesner

2014

Communications in Algebra

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“…The blocks in O are divided into typical blocks (in which, roughly speaking, the super phenomena do not occur) and atypical blocks. The typical blocks were completely described by Gorelik's work [Gor02a,Gor02b]. Indeed the typical blocks are controlled by the Weyl group W of G(3), and Gorelik shows that they are equivalent to some corresponding blocks of the even subalgebra g 0 = G 2 ⊕ sl 2 .…”

Section: Our First Basic Results Is a Classification Of The Blocks In...mentioning

confidence: 99%

Character formulae in category $\mathcal O$ for exceptional Lie superalgebra $G(3)$

Cheng,

Wang

2018

Preprint

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We classify the blocks, compute the Verma flags of tilting and projective modules in the BGG category O for the exceptional Lie superalgebra G(3). The projective injective modules in O are classified. We also compute the Jordan-Hölder multiplicities of the Verma modules in O. Contents 1. Introduction 1 2. Conditions for nonzero Verma flag multiplicities in tilting modules 4 3. Classification of blocks in the BGG category O for G(3) 6 4. Character formulae for tilting modules in O, I 13 5. Character formulae for tilting modules in O, II 18 6. Character formulae for projective modules in O 22 7. Jordan-Hölder multiplicities of Verma modules in O 25 References 27 2010 Mathematics Subject Classification. Primary 17B10.

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“…The last line in the proof of [Go02a, Theorem 9.5] implies we have an isomorphism of bimodules U/J → L(∆(λ), ∆(λ)). Note that strictly speaking, as stated in [Go02a], the results do not cover the exceptional basic classical Lie superalgebras. However, the arguments go through for any basic classical Lie superalgebra.…”

Section: Harish-chandra Bimodulesmentioning

confidence: 93%

The Primitive Spectrum of a Basic Classical Lie Superalgebra

Coulembier

2016

Commun. Math. Phys.

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We prove Conjecture 5.7 in [arXiv:1409.2532, describing all inclusions between primitive ideals for the general linear superalgebra in terms of the Ext 1 -quiver of simple highest weight modules. For arbitrary basic classical Lie superalgebras, we formulate two types of Kazhdan-Lusztig quasi-orders on the dual of the Cartan subalgebra, where one corresponds to the above conjecture. Both orders can be seen as generalisations of the left Kazhdan-Lusztig order on Hecke algebras and are related to categorical braid group actions. We prove that the primitive spectrum is always described by one of the orders, obtaining for the first time a description of the inclusions. We also prove that the two orders are identical if category O admits 'enough' abstract Kazhdan-Lusztig theories. In particular, they are identical for the general linear superalgebra, concluding the proof of the conjecture.

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Annihilation Theorem and Separation Theorem for basic classical Lie superalgebras

Cited by 26 publications

References 23 publications

Whittaker Categories and Whittaker Modules for Lie Superalgebras

Whittaker Categories and Whittaker Modules for Lie Superalgebras

Character formulae in category $\mathcal O$ for exceptional Lie superalgebra $G(3)$

The Primitive Spectrum of a Basic Classical Lie Superalgebra

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