Representations for Lie superalgebras of type C

Shader, Chanyoung Lee

doi:10.1016/s0021-8693(02)00152-7

Cited by 8 publications

(5 citation statements)

References 7 publications

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“…In recent work [14], Musson and Zou have developed a comprehensive crystal base theory for the orthosymplectic Lie superalgebras osp(1, 2r) using the more standard definition of a crystal base, but they do not adopt a tableau approach in their construction. Tableau bases for irreducible osp(1, 2r)-modules are known (see [1], [11]), and it seems likely this case also could be handled by the same methods as in our paper. The algebras osp (1, 2r) are singular in superalgebra theory, because they are the only simple Lie superalgebras whose finite-dimensional modules are completely reducible.…”

Section: Introductionmentioning

confidence: 74%

Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$

Benkart

Kang

Kashiwara

2000

J. Amer. Math. Soc.

181

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Section: Introductionmentioning

confidence: 74%

Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$

Benkart

Kang

Kashiwara

2000

J. Amer. Math. Soc.

181

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“…Consider the case 0 ≤ k ≤ n. In this case using the combinatorial character formula of [Lee,Theorem 3.7] or applying directly (3.3) we see that the character of ker ∆ ⊆ S k (C 2|2n ) is equal to the character of the irreducible module of highest weight (k|0, . .…”

Section: The Composition Factors Of Symmetric Tensorsmentioning

confidence: 99%

A Fock space approach to representation theory of osp(2|2n)

Cheng

Wang

Zhang

2007

Transformation Groups

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A Fock space is introduced that admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimensional tilting and irreducible characters for the Lie superalgebra osp(2|2n). We also determine all the composition factors of the symmetric tensors of the natural osp(2|2n)-module.

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“…We also need some more simple expression for coefficient a λ,µ . We have a λ,µ = a (1) λ,µ a (2) λ,µ where a (1) λ,µ does not depend on p and (i, j) is the added box and a (2)…”

Section: Super Jacobi Polynomialsmentioning

confidence: 99%

Supergroup OSP(2,2n) and super Jacobi polynomials

Movsisyan

Сергеев

2020

Journal of Algebra

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Coefficients of super Jacobi polynomials of type B(1, n) are rational functions in three parameters k, p, q. At the point (−1, 0, 0) these coefficient may have poles. Let us set q = 0 and consider pair (k, p) as a point of A 2 . If we apply blow up procedure at the point (−1, 0) then we get a new family of polynomials depending on parameter t ∈ P. If t = ∞ then we get supercharacters of Kac modules for Lie supergroup OSP (2, 2n) and supercharacters of irreducible modules can be obtained for nonnegative integer t depending on highest weight. Besides we obtained supercharcters of projective covers as specialisation of some nonsingular modification of super Jacobi polynomials.

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Representations for Lie superalgebras of type C

Cited by 8 publications

References 7 publications

Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$

Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$

A Fock space approach to representation theory of osp(2|2n)

Supergroup OSP(2,2n) and super Jacobi polynomials

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