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Pieri algebras and Hibi algebras in representation theory

  • Roger HoweEmail author
Chapter
Part of the Progress in Mathematics book series (PM, volume 257)

Abstract

A class of algebras that unify a variety of calculations in the representation theory of classical groups is discussed. Because of their relation to the classical Pieri Rule, these algebras are called double Pieri algebras. A generalization of the standard monomial theory of Hodge is developed for double Pieri algebras, that uses pairs of semistandard tableaux, rather than a single one. SAGBI theory and toric deformation are key tools. The deformed double Pieri algebras are described using a doubled version of Gelfand–Tsetlin patterns. The approach allows the discussion to avoid dealing with relations between generators.

Keywords

Pieri Rule Classical groups SAGBI theory Standard monomials  Toric deformation 

Mathematics Subject Classification 2010

13A50 15A72 20G05 22E46 22E47 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Yale UniversityNew HavenUSA

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