Alcove path and Nichols-Woronowicz model of the equivariant K-theory of generalized flag varieties

Fomin and Kirillov initiated a line of research into the realization of the cohomology and K-theory of generalized flag varieties G/B as commutative subalgebras of certain noncommutative algebras. This approach has several advantages, which we discuss. This paper contains the most comprehensive resu...

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Bibliographic Details
Published in:International Mathematics Research Notices 2006, Vol.2006 (18)
Main Authors: Lenart, Cristian, Maeno, Toshiaki
Format: Article
Language:English
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Summary:Fomin and Kirillov initiated a line of research into the realization of the cohomology and K-theory of generalized flag varieties G/B as commutative subalgebras of certain noncommutative algebras. This approach has several advantages, which we discuss. This paper contains the most comprehensive result in a series of papers related to the mentioned line of research. More precisely, we give a model for the T-equivariant K-theory of a generalized flag variety KT(G/B) in terms of a certain braided Hopf algebra called the Nichols-Woronowicz algebra. Our model is based on the Chevalley-type multiplication formula for KT(G/B) due to the first author and Postnikov; this formula is stated using certain operators defined in terms of the so-called alcove paths (and the corresponding affine Weyl group). Our model is derived using a type-independent and concise approach.
ISSN:1073-7928
1687-1197
1687-0247
DOI:10.1155/IMRN/2006/78356