The centre of enveloping algebra for Lie superalgebra Q(n, ?)

Сергеев, А. Н.

doi:10.1007/bf00400431

Cited by 58 publications

(40 citation statements)

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“…Some Central Elements. Following Sergeev [20] (where the characteristic zero case was considered), we define certain central elements of Dist(G). Recall from k,l ∈ Dist(G) inductively as follows:…”

Section: Which Case It Is a Self-dual Indecomposable Module With Irrementioning

confidence: 99%

Crystal structures arising from representations of 𝐺𝐿(𝑚|𝑛)

Kujawa

2006

Represent. Theory

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Abstract. This paper provides results on the modular representation theory of the supergroup GL(m|n). Working over a field of arbitrary characteristic, we prove that the explicit combinatorics of certain crystal graphs describe the representation theory of a modular analogue of the Bernstein-Gelfand-Gelfand category O. In particular, we obtain a linkage principle and describe the effect of certain translation functors on irreducible supermodules. Furthermore, our approach accounts for the fact that GL(m|n) has non-conjugate Borel subgroups and we show how Serganova's odd reflections give rise to canonical crystal isomorphisms.

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Section: Which Case It Is a Self-dual Indecomposable Module With Irrementioning

confidence: 99%

Crystal structures arising from representations of 𝐺𝐿(𝑚|𝑛)

Kujawa

2006

Represent. Theory

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“…Observe that for Kac's approach, it is not vital whether g possesses a Cartan matrix or not; for instance, a similar approach is applicable for Q-type algebras (sf. [16] and [2]). A similar method seems to be instrumental in the quantum case.…”

Section: Remarkmentioning

confidence: 99%

The Kac Construction of the Centre of U(g) for Lie Superalgebras

Gorelik¹

2004

JNMP

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“…where ϕ is the Harish-Chandra homomorphism, see [Se3]. Therefore, statement of heading iii) can be reformulated as follows: Let R n be the algebra of polynomials r(t 1 , .…”

Section: Let L ∈ (U(g)mentioning

confidence: 99%

Projective Schur Functions as Bispherical Functions on Certain Homogeneous Superspaces

Сергеев

2003

The Orbit Method in Geometry and Physics

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Abstract. I show that the projective Schur functions may be interpreted as bispherical functions of either the triple (q(n), q(n)⊕ q(n), q(n)), where q(n) is the "odd" (queer) analog of the general linear Lie algebra, or the triple (pe(n), gl(n|n), pe(n)), where pe(n) is the periplectic Lie superalgebra which preserves the nondegenerate odd bilinear form (either symmetric or skew-symmetric). Making use of this interpretation I characterize projective Schur functions as common eigenfunctions of an algebra of differential operators.

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The centre of enveloping algebra for Lie superalgebra Q(n, ?)

Cited by 58 publications

References 1 publication

Crystal structures arising from representations of 𝐺𝐿(𝑚|𝑛)

Crystal structures arising from representations of 𝐺𝐿(𝑚|𝑛)

The Kac Construction of the Centre of U(g) for Lie Superalgebras

Projective Schur Functions as Bispherical Functions on Certain Homogeneous Superspaces

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