Alcove path and Nichols-Woronowicz model of the equivariant K-theory of generalized flag varieties
Lenart, Cristian · Maeno, Toshiaki
Original · EN
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 so-called alcove paths (and the corresponding affine Weyl group). Our model is derived using a type-independent and concise approach.
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