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T-equivariant K-theory of generalized flag varieties. (English) Zbl 0731.55005
To any generalized Cartan matrix, A, one associates a Kac-Moody algebra, $${\mathcal G}(A)$$, over $${\mathbb{C}}$$ and a group, $$G=G(A)$$. Let K be the standard maximal compact subgroup of G(A). Let H and B denote a complex maximal torus and a Borel subgroup, respectively. If $$T=H\cap K$$, the authors show how to calculate the T-equivariant K-group, $$K_ T(G/B)$$, in terms of the combinatorial algebra of the Weyl group.
These results extend the results of J. McLeod and the reviewer in the classical case [J. McLeod, Lect. Notes Math. 741, 316-333 (1979; Zbl 0426.55006)]. In Adv. Math. 62, 187-237 (1986; Zbl 0641.17008), the authors completed a similar algebraization for $$H^*(G/B)$$.

##### MSC:
 55N15 Topological $$K$$-theory 19L47 Equivariant $$K$$-theory
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