Generalized Young Tableaux and the General Linear Group

King, Ronald C.

doi:10.1063/1.1665059

Cited by 51 publications

(16 citation statements)

References 12 publications

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“…. This is the same definition of the conjugate fundamental representation as for SU (N ), and following [Kin70] can be associated the single dotted Young tableau .…”

Section: Su(2|2) Representations and Supertableauxmentioning

confidence: 99%

Young supertableaux and the large ${ \mathcal N }=4$ superconformal algebra

Fearn¹

2019

Phys. Scr.

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In this paper we consider unitary highest weight irreducible representations of the 'Large' N = 4 superconformal algebra A γ in the Ramond sector as infinite-dimensional graded modules of its zero mode subalgebra, su(2|2). We describe how representations of su(2|2) may be classified using Young supertableaux, and use the decomposition of A γ as an su(2|2) module to discuss the states which contribute to the supersymmetric index I 1 , previously proposed in the literature by Gukov, Martinec, Moore and Strominger.

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“…. This is the same definition of the conjugate fundamental representation as for SU (N ), and following [Kin70] can be associated the single dotted Young tableau .…”

Section: Su(2|2) Representations and Supertableauxmentioning

confidence: 99%

Young supertableaux and the large ${ \mathcal N }=4$ superconformal algebra

Fearn¹

2019

Phys. Scr.

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“…, (9) which has been used to define the rational [10], or mixed tensor [4] characters s λ;μ (x) of the general linear group GL(m) of highest weight…”

Section: Introductionmentioning

confidence: 99%

Extended Bressoud–Wei and Koike skew Schur function identities

Hamel

King

2011

Journal of Combinatorial Theory, Series A

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The Jacobi-Trudi identity expresses a skew Schur function as a determinant of complete symmetric functions. Bressoud and Wei extend this idea, introducing an integer parameter t −1 and showing that signed sums of skew Schur functions of a certain shape are expressible once again as a determinant of complete symmetric functions. Koike provides a Jacobi-Trudi-style definition of universal rational characters of the general linear group and gives their expansion as a signed sum of products of Schur functions in two distinct sets of variables. Here we extend Bressoud and Wei's formula by including an additional parameter and extending the result to the case of all integer t. Then we introduce this parameter idea to the Koike formula, extending it in the same way. We prove our results algebraically using Laplace determinantal expansions.

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“…There are 10 infinite families of such pairs [HTW1]. A substantial body of literature exists which gives combinatorial descriptions of the branching multiplicities for classical symmetric pairs [LR,Li1,Li2,Li3,Ki1,Ki2,Ki3,Ki4,BKW,Ne,Ko,KT,Su,HTW2]. In [HTW1], a project was begun to develop a more refined understanding of branching laws for classical symmetric pairs by the study of branching algebras, multigraded algebras which encode all branching information for a pair (G, K) of group and subgroup in a single algebraic structure.…”

Section: Introductionmentioning

confidence: 99%