A presentation of the double Pieri algebra

Kim, Sangjib

doi:10.1016/j.jpaa.2017.04.008

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Cited by 3 publications

References 13 publications

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Hibi Algebras and Representation Theory

Kim

Protsak

2018

Acta Math Vietnam

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This paper gives a survey on the relation between Hibi algebras and representation theory. The notion of Hodge algebras or algebras with straightening laws has been proved to be very useful to describe the structure of many important algebras in classical invariant theory and representation theory [2,5,6,10,33]. In particular, a special type of such algebras introduced by Hibi [12] provides a nice bridge between combinatorics and representation theory of classical groups. We will examine certain poset structures of Young tableaux and affine monoids, Hibi algebras in toric degenerations of flag varieties, and their relations to polynomial representations of the complex general linear group.2010 Mathematics Subject Classification. 13A50, 13F50, 20G05, 05E10, 05E15.

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Hibi Algebras and Representation Theory

Kim

Protsak

2018

Acta Math Vietnam

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On the structures of hive algebras and tensor product algebras for general linear groups of low rank

Kim

Park

2019

Int. J. Algebra Comput.

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The tensor product algebra TA(n) for the complex general linear group GL(n), introduced by Howe et al., describes the decomposition of tensor products of irreducible polynomial representations of GL(n). Using the hive model for the Littlewood-Richardson coefficients, we provide a finite presentation of the algebra TA(n) for n = 2, 3, 4 in terms of generators and relations, thereby giving a description of highest weight vectors of irreducible representations in the tensor products. We also compute the generating function of certain sums of Littlewood-Richardson coefficients.2010 Mathematics Subject Classification. 20G05, 13A50, 05E15.

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Hibi algebras and representation theory

Kim¹,

Protsak²

2018

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A presentation of the double Pieri algebra

Cited by 3 publications

References 13 publications

Hibi Algebras and Representation Theory

Hibi Algebras and Representation Theory

On the structures of hive algebras and tensor product algebras for general linear groups of low rank

Hibi algebras and representation theory

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