Let G be a Kac—Moody group with Borel subgroup B and compact maximal torus T. Analogous to Kostant and Kumar [Kostant, B. & 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 Ψ, which, we prove, is “canonically” isomorphic with the T-equivariant K-theory KT(G/B) of G/B. Now KT(G/B), apart from being an algebra over KT(pt.) ≈ A(T), also has a Weyl group action and, moreover, KT(G/B) admits certain operators {Dw}w[unk]W similar to the Demazure operators defined on A(T). We prove that these structures on KT(G/B) come naturally from the ring Y. By “evaluating” the A(T)-module Ψ 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.
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机译：令G为带有Borel子组B和紧致最大圆环T的Kac-Moody组。类似于Kostant和Kumar [Kostant，B.＆Kumar，S.（1986）Proc.Natl.Acad.Sci.USA 90：5873-5877。 Natl。学院科学[USA 83，1543-1545]，我们仅根据Weyl基团W（与G相关联）及其对T的作用定义了一个特定的环Y。通过对Y进行二元化，我们得到了另一个环Ψ，我们证明它是“与G / B的T等价K理论KT（G / B）同构。现在 KT （ G / B ），除了是 KT （pt。）≈ A （ T ），也具有Weyl基团作用，此外， KT （ G / B < / em>）允许某些运算符{ Dw } w [unk] W 类似于在 A （ T ）。我们证明 KT （ G / B ）上的这些结构自然来自环 Y 。通过“评估”位于1的 A （ T ）-模块we，我们恢复了 K （ G / < em> B ）以及上述结构。我们认为，本文的许多结果在有限情况下也是新的（即 G 是C上的有限维半简单群）。
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