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Buchsbaum, David A.

doi:10.1007/978-1-4614-5292-8_7

Cited by 1 publication

(4 citation statements)

References 22 publications

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“…The function HS λ (x, y) is given by summing certain monomials corresponding to (m|n)-semistandard tableaux. In particular, by 6.11 of [1] there is (4) HS λ (x, y) = µ<λ ν…”

Section: Operator τ and Its Action On Littlewood-richardson Tableauxmentioning

confidence: 99%

“…To illustrate the above notation, consider m = n = 3, λ = (6, 4, 4, 3, 1), λ + =(6,4,4), λ − = (3, 1), (λ − ) ′ = (2, 1, 1), µ = (4, 2, 1) and ν =(5,4,2). Then the tableaua a a a b b a a b b a b b b c c c c is such that the entries a represent the shape µ; entries b represent the shape λ + /µ; and entries c represent the shape (λ − ) ′ .…”

mentioning

confidence: 99%

“…Let m = n = 3, λ = (5, 4, 4|3, 2, 1) and µ = (2, 2, 1) which implies λ ′ = (6, 5, 4, 3, 1), µ ′ = (3, 2). Let ν =(5,5,4) and T + be given as Then w(T + ) = 45546656 and the tableau T − is…”

mentioning

confidence: 99%

“…According to Theorem 4.4 of [25] (see also Section 5 of [24] or Section 5.7 of [4]), there is a basis for bipermanents of fixed skew shape and content given by bipermanents corresponding to semistandard tableaux. This statement is a generalization of the classical result of [7].…”

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Even-primitive vectors in induced supermodules for general linear supergroups and in costandard supermodules for Schur superalgebras

Marko

2019

J Algebr Comb

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Let G = GL(m|n) be the general linear supergroup over an algebraically closed field K of characteristic zero and let Gev = GL(m) × GL(n) be its even subsupergroup. The induced supermodule H 0 G (λ), corresponding to a dominant weight λ of G, can be represented as H 0Vn is a tensor product of the dual of the natural GL(m)-module Vm and the natural GL(n)-module Vn, and Λ(Y ) is the exterior algebra of Y . For a dominant weight λ of G, we construct explicit Gev-primitive vectors in H 0 G (λ). Related to this, we give explicit formulas for Gev -primitive vectors of the supermodules H 0 Gev (λ) ⊗ ⊗ k Y . Finally, we describe a basis of Gev -primitive vectors in the largest polynomial subsupermodule ∇(λ) of H 0 G (λ) (and therefore in the costandard supermodule of the corresponding Schur superalgebra S(m|n)). This yields a description of a basis of Gev-primitive vectors in arbitrary induced supermodule H 0 G (λ).2010 Mathematics Subject Classification. 15A15 (primary) 17A70, 20G05, 15A72, 13A50, 05E15 (secondary).

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“…The function HS λ (x, y) is given by summing certain monomials corresponding to (m|n)-semistandard tableaux. In particular, by 6.11 of [1] there is (4) HS λ (x, y) = µ<λ ν…”

Section: Operator τ and Its Action On Littlewood-richardson Tableauxmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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