Pieri algebras for the orthogonal and symplectic groups

Kim, Sangjib; Lee, Soo Teck

doi:10.1007/s11856-012-0105-1

Cited by 11 publications

(2 citation statements)

References 19 publications

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“…[KL,Proposition 4.1] For 2(k + p) < n, the iterated Pieri algebra A n,k,p for O n is isomorphic as an algebra and A n × A k × A p module to…”

Section: It Is a Module For Omentioning

confidence: 99%

Double Pieri algebras and iterated Pieri algebras for the classical groups

Howe¹,

Kim²,

Lee³

2017

American Journal of Mathematics

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Abstract. We study iterated Pieri rules for representations of classical groups. That is, we consider tensor products of a general representation with multiple factors of representations corresponding to one-rowed Young diagrams (or in the case of the general linear group, also the duals of these). We define iterated Pieri algebras, whose structure encodes the irreducible decompositions of such tensor products. We show that there is a single family of algebras, which we call double Pieri algebras, and which can be used to describe the iterated Pieri algebras for all three families of classical groups. Furthermore, we show that the double Pieri algebras have flat deformations to Hibi rings on explicitly described posets.

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“…[KL,Proposition 4.1] For 2(k + p) < n, the iterated Pieri algebra A n,k,p for O n is isomorphic as an algebra and A n × A k × A p module to…”

Section: It Is a Module For Omentioning

confidence: 99%

Double Pieri algebras and iterated Pieri algebras for the classical groups

Howe¹,

Kim²,

Lee³

2017

American Journal of Mathematics

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“…With a similar philosophy, [19] and [22] study tensor products of representations for the classical groups with explicit highest weight vectors. By degenerating the multi-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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Pieri algebras and Hibi algebras in representation theory

Howe

2014

Symmetry: Representation Theory and Its Applications

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Pieri algebras for the orthogonal and symplectic groups

Cited by 11 publications

References 19 publications

Double Pieri algebras and iterated Pieri algebras for the classical groups

Double Pieri algebras and iterated Pieri algebras for the classical groups

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

Pieri algebras and Hibi algebras in representation theory

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