Combinatorial extension of stable branching rules for classical groups

Kwon, Jae-Hoon

doi:10.1090/tran/7104

Cited by 13 publications

(11 citation statements)

References 34 publications

(65 reference statements)

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“…In this subsection, we review another combinatorial model of Bpλq in types B n and C n introduced in [19]. We will follow the convention in [18], where the definition of this model is slightly different from [19]. For 0 ď a ă n, let…”

Section: 2mentioning

confidence: 99%

“…More precisely, if T " l S for some S P SST rns pγq with γ 1 ă ℓ, then pT tail q " T body . This phenomenon is closely related to so-called a stable branching rule, which is discussed in [18] with more details.…”

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confidence: 92%

“…14 and 3.19), where each single column on the side of T λ corresponds to a monomial in a spin representation. We may call T λ a spinor model of Bpλq for this reason (see [18,19,20] for other applications).…”

Section: Introductionmentioning

confidence: 99%

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Lusztig data of Kashiwara–Nakashima tableaux in types B and C

Kwon

2018

Journal of Algebra

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We provide an explicit combinatorial description of the embedding of the crystal of Kashiwara-Nakashima tableaux in types B and C into that of i-Lusztig data associated to a family of reduced expressions i of the longest element w0. The description of the embedding is simple and elementary using only the Schützenberger's jeu de taquin and RSK algorithm. A spinor model for classical crystals plays an important role as an intermediate object connecting Kashiwara-Nakashima tableaux and Lusztig data.2010 Mathematics Subject Classification. 17B37, 22E46, 05E10.(1.2)where r " xω λ , h n y, T λ is another tableau model of Bpω λ q introduced in [19,20], and V λ is the crystal of a parabolic Verma module with respect to a maximal Levi subalgebra l of type A n´1 in g [16,17].

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Section: 2mentioning

confidence: 99%

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confidence: 92%

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Lusztig data of Kashiwara–Nakashima tableaux in types B and C

Kwon

2018

Journal of Algebra

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“…We solve a problem posed by Sundaram in her 1986 thesis [12] concerning the direct-sum-decomposition into irreducibles of tensor powers of the defining representation (also known as vector representation) of the special orthogonal group SO (3). In particular, our main result is a bijection for SO(3) between so called vacillating tableaux and pairs consisting of an orthogonal Littlewood-Richardson tableau (recently introduced by Kwon [5]) and a standard Young tableau.…”

Section: Introductionmentioning

confidence: 99%

A Sundaram type Bijection for SO(3): Vacillating Tableaux and Pairs of Standard Young Tableaux and Orthogonal Littlewood-Richardson Tableaux

Jagenteufel

2018

Electron. J. Combin.

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We present a bijection between vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau for the special orthogonal group SO(2k + 1). This bijection is motivated by the direct-sum-decomposition of the rth tensor power of the defining representation of SO(2k + 1). To formulate it, we use Kwon's orthogonal Littlewood-Richardson tableaux and introduce new alternative tableaux they are in bijection with.Moreover we use a suitably defined descent set for vacillating tableaux to determine the quasi-symmetric expansion of the Frobenius characters of the isotypic components.

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“…The branching problem is an important problem in representation theory, algebraic combinatorics and orthogonal polynomials on root systems, see e.g., [8,9,15,16,18,19,21,22,23,24,25,26,29,31,34,35,47]. In this paper we are interested in q, t-analogues of multiplicity-free branching rules such as (1.2) and (1.4).…”

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confidence: 99%