Parabolic Category for Periplectic Lie Superalgebras

CHEN, CHIH-WHI; Peng, Yung-Ning

doi:10.1007/s00031-021-09682-9

Cited by 3 publications

(2 citation statements)

References 39 publications

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“…We recall from [Se2,Section 5] Proof. By [CP,Corollary 4.4] we have [ M (λ) : L(µ)] = [M (λ) : L(µ)], for any µ ∈ h * (ass also [Se2,Corollary 5.8]). The conclusion follows Theorem 18.…”

Section: 32mentioning

confidence: 97%

Whittaker modules for classical Lie superalgebras

Chen

2021

Preprint

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We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. We establish a type of Miličić-Soergel equivalence of a category of Whittaker modules and a category of Harish-Chandra bimodules. For classical Lie superalgebras of type I, we reduce the problem of composition factors of standard Whittaker modules to that of Verma modules in their BGG categories O. As a consequence, the composition series of standard Whittaker modules over the general linear Lie superalgebras gl(m|n) and the ortho-symplectic Lie superalgebras osp(2|2n) can be computed via the Kazhdan-Lusztig combinatorics.

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Section: 32mentioning

confidence: 97%

Whittaker modules for classical Lie superalgebras

Chen

2021

Preprint

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“…The endomorphism algebras in this supercategory give a diagrammatic realization of Moon's algebra. Since then, there has been substantial work applying diagrammatic, combinatorial, and categorical techniques to the study of p(n) and Moon's algebra (see [2][3][4][8][9][10][11][12] and the references therein). The present paper further develops this approach to the representation theory of p(n).…”

Section: Introductionmentioning

confidence: 99%

Webs of type P

Davidson,

Kujawa,

Muth

2023

Can. J. Math.-J. Can. Math.

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This paper introduces type P web supercategories. They are defined as diagrammatic monoidal ${\mathbb {k}}$ -linear supercategories via generators and relations. We study the structure of these categories and provide diagrammatic bases for their morphism spaces. We also prove these supercategories provide combinatorial models for the monoidal supercategory generated by the symmetric powers of the natural module and their duals for the Lie superalgebra of type P.

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Howe Duality of Type P

Davidson,

Kujawa,

Muth

2024

Transformation Groups

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We establish classical and categorical Howe dualities between the Lie superalgebras $$\mathfrak {p}(m)$$ p ( m ) and $$\mathfrak {p}(n)$$ p ( n ) , for $$m,n \ge 1$$ m , n ≥ 1 . We also describe a presentation via generators and relations as well as a Kostant $$\mathbb {Z}$$ Z -form for the universal enveloping superalgebra $$U(\mathfrak {p}(m))$$ U ( p ( m ) ) .

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Parabolic Category for Periplectic Lie Superalgebras

Cited by 3 publications

References 39 publications

Whittaker modules for classical Lie superalgebras

Whittaker modules for classical Lie superalgebras

Webs of type P

Howe Duality of Type P

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