Canonical bases and self-evacuating tableaux
type: Item
instance of: scholarly article
title: Canonical bases and self-evacuating tableaux
zbMATH Open document ID: 0869.17011
DOI: 10.1215/S0012-7094-96-08224-1
author: John R. Stembridge
published in: Duke Mathematical Journal
publication date: 1997-06-06T00:00:00Z
review text: This article is centered around the problem of enumerating semi-standard and standard tableaux fixed by an involution defined by Schützenberger and called ``evacuation''. The author obtains several representation theoretic expressions for these numbers. For this he first gives an expression in representation theoretic terms for the number of fixed points of Lusztig's involution on the canonical basis of an irreducible finite dimensional representation. By work of \textit{A. Berenstein} and \textit{A. Zelevinsky} [Duke Math. J. 82, 473-502 (1996)] Lusztig's involution corresponds in type \(A\) to Schützenberger's under a suitable parametrization of the canonical basis by semi-standard tableaux. This then leads to the main results.
reviewed by: Wolfgang Soergel
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 908702
zbMATH Keywords: Schützenberger involution
zbMATH Keywords: evacuation
MaRDI profile type: Publication
cites work: Canonical bases for the quantum group of type \(A_r\) and piecewise-linear combinatorics
cites work: Q3994903
cites work: Splitting the square of a Schur function into its symmetric and antisymmetric parts
cites work: On the equality of two plane partition correspondences
cites work: Relations between Young's natural and the Kazhdan-Lusztig representations of \(S_ n\)
cites work: Q4029512
cites work: Introduction to Lie Algebras and Representation Theory
cites work: Q3952291
cites work: Q4040877
cites work: Representations of Coxeter groups and Hecke algebras
cites work: Q4297378
cites work: Q4057549
cites work: On Macdonald's \(\eta\)-function formula, the Laplacian and generalized exponents
cites work: Self-complementary plane partitions by Proctor's minuscule method
cites work: Canonical Bases Arising from Quantized Enveloping Algebras. II
cites work: Q3947818
cites work: On the Left Cell Representations of Iwahori-Hecke Algebras of Finite Coxeter Groups
cites work: The Kazhdan-Lusztig cells in certain affine Weyl groups
cites work: Symmetries of plane partitions
cites work: A Schensted algorithm for rim hook tableaux
cites work: On minuscule representations, plane partitions and involutions in complex Lie groups
description: scientific article; zbMATH DE number 908702