Pieri algebras for the orthogonal and symplectic groups

Kim, Sangjib; Lee, Soo Teck

doi:10.48550/arxiv.0907.1336

Cited by 4 publications

(2 citation statements)

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“…The recent papers [16,17,18] and their sequels construct algebras encoding branching rules of representations of the classical groups, and then study their standard monomial bases and toric degenerations. With a similar philosophy, [19] and [22] study tensor products of representations for the classical groups with explicit highest weight vectors. By degenerating the muti-homogeneous coordinate rings of the flag varieties, [20] and [21] describe weight vectors of the classical groups in terms of the Gelfand-Tsetlin polyhedral cone.…”

Section: Introductionmentioning

confidence: 99%

The nullcone in the multi-vector representation of the symplectic group and related combinatorics

Kim

2010

Journal of Combinatorial Theory, Series A

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We study the nullcone in the multi-vector representation of the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring of the nullcone, we describe a toric degeneration and standard monomial theory of the nullcone in terms of double tableaux and integral points in a convex polyhedral cone.

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Section: Introductionmentioning

confidence: 99%

The nullcone in the multi-vector representation of the symplectic group and related combinatorics

Kim

2010

Journal of Combinatorial Theory, Series A

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“…We remark that this Hibi algebra structure in branching problems has interesting counterparts in tensor product decomposition problems, which can be explained by reciprocity properties between branchings and tensor products in representation theory. For this direction, we refer readers to [HL07,HKL,KL].…”

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Distributive lattices, affine semigroups, and branching rules of the classical groups

Kim

2012

Journal of Combinatorial Theory, Series A

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We study algebras encoding stable range branching rules for the pairs of complex classical groups of the same type in the context of toric degenerations of spherical varieties. By lifting affine semigroup algebras constructed from combinatorial data of branching multiplicities, we obtain algebras having highest weight vectors in multiplicity spaces as their standard monomial type bases. In particular, we identify a family of distributive lattices and their associated Hibi algebras which can uniformly describe the stable range branching algebras for all the pairs we consider.2000 Mathematics Subject Classification. 20G05, 05E15.

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The nullcone in the multi-vector representation of the symplectic group and related combinatorics

Kim¹

2009

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Pieri algebras for the orthogonal and symplectic groups

Cited by 4 publications

References 6 publications

The nullcone in the multi-vector representation of the symplectic group and related combinatorics

The nullcone in the multi-vector representation of the symplectic group and related combinatorics

Distributive lattices, affine semigroups, and branching rules of the classical groups

The nullcone in the multi-vector representation of the symplectic group and related combinatorics

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