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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Large Schubert varieties
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by Michel Brion and Patrick Polo
Represent. Theory 4 (2000), 97-126
Published electronically: February 23, 2000


For a semisimple adjoint algebraic group $G$ and a Borel subgroup $B$, consider the double classes $BwB$ in $G$ and their closures in the canonical compactification of $G$; we call these closures large Schubert varieties. We show that these varieties are normal and Cohen-Macaulay; we describe their Picard group and the spaces of sections of their line bundles. As an application, we construct geometrically a filtration à la van der Kallen of the algebra of regular functions on $B$. We also construct a degeneration of the flag variety $G/B$ embedded diagonally in $G/B\times G/B$, into a union of Schubert varieties. This yields formulae for the class of the diagonal of $G/B\times G/B$ in $T$-equivariant $K$-theory, where $T$ is a maximal torus of $B$.
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Bibliographic Information
  • Michel Brion
  • Affiliation: Université de Grenoble I, Département de Mathématiques, Institut Fourier, UMR 5582 du CNRS, 38402 Saint-Martin d’Hères Cedex, France
  • MR Author ID: 41725
  • Email:
  • Patrick Polo
  • Affiliation: Université Paris Nord, Département de Mathématiques, L.A.G.A., UMR 7539 du CNRS, 93430 Villetaneuse, France
  • Email:
  • Received by editor(s): April 27, 1999
  • Received by editor(s) in revised form: October 9, 1999
  • Published electronically: February 23, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Represent. Theory 4 (2000), 97-126
  • MSC (2000): Primary 14M15, 14L30, 20G05, 19E08
  • DOI:
  • MathSciNet review: 1789463