English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let G be a Kac-Moody group with Borel subgroup B and compact maximal torus T. Analogous to Kostant and Kumar [Kostant, B. &amp; Kumar, S. (1986) Proc. Natl. Acad. Sci. USA 83, 1543-1545], we define a certain ring Y, purely in terms of the Weyl group W (associated to G) and its action on T. By dualizing Y we get another ring Psi, which, we prove, is "canonically" isomorphic with the T-equivariant K-theory K(T)(G/B) of G/B. Now K(T)(G/B), apart from being an algebra over K(T)(pt.) approximately A(T), also has a Weyl group action and, moreover, K(T)(G/B) admits certain operators {D(w)}w[unk]W similar to the Demazure operators defined on A(T). We prove that these structures on K(T)(G/B) come naturally from the ring Y. By "evaluating" the A(T)-module Psi at 1, we recover K(G/B) together with the above-mentioned structures. We believe that many of the results of this paper are new in the finite case (i.e., G is a finite-dimensional semisimple group over C) as well.

T -equivariant K -theory of generalized flag varieties