Tilting modules for classical Lie superalgebras

Chen, Chih-Whi; Cheng, Shun‐Jen; Coulembier, Kevin

doi:10.1112/jlms.12395

Cited by 19 publications

(36 citation statements)

References 41 publications

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“…We also remark that in [CCC, Section 1.4] the Cartan subalgebra is defined as g 0 and not necessarily even in [CC]. For a given Borel subalgebra b of g0, every Borel subalgebra of g is conjugate to one which has b as underlying even subalgebra by [CCC,Section 1.3].…”

Section: Throughout the Present Paper We Fix A Triangular Decompositi...mentioning

confidence: 99%

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Annihilator ideals and blocks of Whittaker modules over quasireductive Lie superalgebras

Chen¹

2021

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We extend Kostant's result on annihilator ideals of non-singular simple Whittaker modules over Lie algebras to (possibly singular) simple Whittaker modules over Lie superalgebras. We describe these annihilator ideals in terms of certain primitive ideals coming from the category O for quasireductive Lie superalgebras.To determine these annihilator ideals, we develop annihilator-preserving equivalences between certain full subcategories of the Whittaker category N and the categories of certain projectively presentable modules in the category O. These equivalences lead to a classification of simple Whittaker modules that lie in the integral central blocks when restricted to the even subalgebra. We make a connection between the linkage classes of integral blocks of O and of N . In particular, they can be computed via Kazhdan-Lusztig combinatorics for Lie superalgebras of type gl and osp. We then give a description of the integral blocks of the category N of Whittaker modules for Lie superalgebras gl(m|n), osp(2|2n) and pe(n). Contents 1. Introduction 1 2. Preliminaries 8 3. Realizations of completion and twisting functors 14 4. The category of projectively presentable modules 18 5. Annihilator ideals of simple Whittaker modules 23 6. Linkage principle of the category N Z for gl(m|n), osp(2|2n) and pe(n) 32 References 40

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Section: Throughout the Present Paper We Fix A Triangular Decompositi...mentioning

confidence: 99%

“…Similarly, we will use M (λ) instead of M (λ, i), for any (λ, i) ∈ h * × Z 2 . It turns out that (O, ≤) is a highest weight category with standard objects M (λ) by [CCC,Theorem 3.1]. Also, we denote by P (λ) and P (λ) (resp.…”

Section: Bgg Categorymentioning

confidence: 99%

Annihilator ideals and blocks of Whittaker modules over quasireductive Lie superalgebras

Chen¹

2021

Preprint

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show abstract

“…Also, we refer to the subalgebras b := h + n + and b r := b0 + g −1 as standard Borel subalgebra and reverse Borel subalgebra, respectively. There subalgebras are all Borel-Penkov-Serganova subalgebras in the sense of [PS1] and [Mu2,Section 3.2]; see also [CCC,Sections 1.3,1.4] for more details.…”

Section: Preliminariesmentioning

confidence: 99%

“…. By [CCC,Theorem 3.1] (O, ≤) is a highest weight category with standard objects M (λ). Also, we denote by P (λ) and P (λ) the projective covers of L(λ) and L(λ) in O0 and O, respectively.…”

Section: Bgg Category Omentioning

confidence: 99%