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Representation Theory

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A geometric approach to Standard Monomial Theory

Authors: M. Brion and V. Lakshmibai
Journal: Represent. Theory 7 (2003), 651-680
MSC (2000): Primary 14M15, 20G05, 14L30, 14L40
Published electronically: November 24, 2003
MathSciNet review: 2017071
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Abstract: We obtain a geometric construction of a ``standard monomial basis'' for the homogeneous coordinate ring associated with any ample line bundle on any flag variety. This basis is compatible with Schubert varieties, opposite Schubert varieties, and unions of intersections of these varieties. Our approach relies on vanishing theorems and a degeneration of the diagonal; it also yields a standard monomial basis for the multi-homogeneous coordinate rings of flag varieties of classical type.

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Additional Information

M. Brion
Affiliation: Institut Fourier, UMR 5582 du CNRS, F-38402 Saint-Martin d’Hères Cedex

V. Lakshmibai
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115-5096

Received by editor(s): November 8, 2001
Received by editor(s) in revised form: September 12, 2003
Published electronically: November 24, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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