Symplectic and orthogonal Robinson-Schensted algorithms
type: Item
instance of: scholarly article
title: Symplectic and orthogonal Robinson-Schensted algorithms
zbMATH Open document ID: 1103.22004
author: Peter E. Trapa
published in: Journal of Algebra
publication date: 2005-05-04T00:00:00Z
review text: Let \(G_{\mathbb{R}}\) be a linear reductive real Lie group with maximal compact subgroup \(K_{\mathbb{R}}\). Let \(K\) be the complexification of \(K_{\mathbb{R}}\) and let \(\mathcal{B}\) denote the flag variety of the complexified Lie algebra \(\mathfrak{g}\) of \(G_{\mathbb{R}}\). Let \(Q\) be a \(K\)-orbit on \(\mathcal{B}\) and denote by \(\mu\) the moment map from \(T^*\mathcal{B}\) to the nilpotent cone \(\mathcal{N}(\mathfrak{g}^*)\). The paper under review gives a simple algorithm to compute the image under \(\mu\) of the conormal bundle \(T_Q^*(\mathcal{B})\) explicitly when \(G_{\mathbb{R}}\) is \(\text{Sp}(2n,\mathbb{R})\) or \(O(p,q)\). Moreover, for a generic point \(\xi\) of the image of \(\mu\), the author obtains a new parametrization of the orbits of the component group of the centralizer of \(\xi\) in \(G\) on the irreducible components of the Springer fiber \(\mu^{-1}(\xi)\) in terms of the domino tableaux. This parametrization is closely related to the computation of annihilators of the derived functor modules for the groups under consideration. Similar questions were previously treated by A. Yamamoto, but her algorithms are different and not as well suited for the analysis of the components of the Springer fiber. The computations of this paper have very nice combinatorial interpretations as generalizations of the classical Robinson-Schensted algorithm.
reviewed by: Pavle Pandžić
Mathematics Subject Classification ID: 22E15
zbMATH DE Number: 2164788
zbMATH Keywords: representation
zbMATH Keywords: real reductive group
zbMATH Keywords: Young tableau
zbMATH Keywords: Robinson-Schensted algorithm
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.07.026
OpenAlex ID: W2013913704
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DOI: 10.1016/J.JALGEBRA.2003.07.026
description: scientific article; zbMATH DE number 2164788