Large Schubert varieties
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- by Michel Brion and Patrick Polo
- Represent. Theory 4 (2000), 97-126
- DOI: https://doi.org/10.1090/S1088-4165-00-00069-8
- Published electronically: February 23, 2000
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Abstract:
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 $B$.References
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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: Michel.Brion@ujf-grenoble.fr
- Patrick Polo
- Affiliation: Université Paris Nord, Département de Mathématiques, L.A.G.A., UMR 7539 du CNRS, 93430 Villetaneuse, France
- Email: polo@math.univ-paris13.fr
- 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: https://doi.org/10.1090/S1088-4165-00-00069-8
- MathSciNet review: 1789463