Hibi Algebras and Representation Theory

Hibi Algebras and Representation Theory Acta Math Vietnam https://doi.org/10.1007/s40306-018-0263-2 1 2 Sangjib Kim · Victor Protsak Received: 21 February 2018 / Accepted: 2 April 2018 © Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018 Abstract This paper gives a survey on the relation between Hibi algebras and represen- tation 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 (Bruns and Herzog 1993;DeConcinietal. 1982; Eisenbud 1980; Gonciulea and Lakshmibai 2001; Seshadri 2007). In particular, a special type of such algebras introduced by Hibi (1987) provides a nice bridge between combina- torics 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. Keywords Algebras with straightening laws · Hibi algebras · Distributive lattices · Affine semigroups · Gelfand-Tsetlin patterns · Representations · General linear groups Mathematics Subject Classification (2010) 13A50 · 13F50 · 20G05 · 05E10 · 05E15 1 Young Tableaux and Gelfand-Tsetlin Poset In http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Vietnamica Springer Journals

Hibi Algebras and Representation Theory

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Publisher
Springer Singapore
Copyright
Copyright © 2018 by Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.
Subject
Mathematics; Mathematics, general
ISSN
0251-4184
eISSN
2315-4144
D.O.I.
10.1007/s40306-018-0263-2
Publisher site
See Article on Publisher Site

Abstract

Acta Math Vietnam https://doi.org/10.1007/s40306-018-0263-2 1 2 Sangjib Kim · Victor Protsak Received: 21 February 2018 / Accepted: 2 April 2018 © Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018 Abstract This paper gives a survey on the relation between Hibi algebras and represen- tation 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 (Bruns and Herzog 1993;DeConcinietal. 1982; Eisenbud 1980; Gonciulea and Lakshmibai 2001; Seshadri 2007). In particular, a special type of such algebras introduced by Hibi (1987) provides a nice bridge between combina- torics 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. Keywords Algebras with straightening laws · Hibi algebras · Distributive lattices · Affine semigroups · Gelfand-Tsetlin patterns · Representations · General linear groups Mathematics Subject Classification (2010) 13A50 · 13F50 · 20G05 · 05E10 · 05E15 1 Young Tableaux and Gelfand-Tsetlin Poset In

Journal

Acta Mathematica VietnamicaSpringer Journals

Published: Jun 5, 2018

References

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