Duke Mathematical Journal

K-théorie équivariante des tours de Bott. Application à la structure multiplicative de la K-théorie équivariante des variétés de drapeaux

Matthieu Willems

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Abstract

(Equivariant K-theory of Bott towers. Application to the multiplicative structure of the equivariant K-theory of flag varieties)

We construct a basis of the equivariant K-theory of Bott towers, and we describe precisely the multiplicative structure of these algebras. We deduce similar results for Bott-Samelson varieties. Thanks to the link between flag varieties and Bott-Samelson varieties, we give a method to compute the structure constants of the equivariant K-theory of flag varieties in the basis constructed by Kostant and Kumar in [18]

Article information

Source
Duke Math. J., Volume 132, Number 2 (2006), 271-309.

Dates
First available in Project Euclid: 16 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1142517219

Digital Object Identifier
doi:10.1215/S0012-7094-06-13223-4

Mathematical Reviews number (MathSciNet)
MR2219259

Zentralblatt MATH identifier
1118.19002

Subjects
Primary: 19L47: Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14M25: Toric varieties, Newton polyhedra [See also 52B20]

Citation

Willems, Matthieu. $K$ -théorie équivariante des tours de Bott. Application à la structure multiplicative de la $K$ -théorie équivariante des variétés de drapeaux. Duke Math. J. 132 (2006), no. 2, 271--309. doi:10.1215/S0012-7094-06-13223-4. https://projecteuclid.org/euclid.dmj/1142517219


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