T-equivariant K-theory of generalized flag varieties. (English) Zbl 0731.55005

Kostant, Bertram; Kumar, Shrawan

J. Differ. Geom. 32, No. 2, 549-603 (1990).

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 \(H^*(G/B)\).

Reviewer: V.P.Snaith (Hamilton/Ontario)

MSC:

55N15	Topological \(K\)-theory
19L47	Equivariant \(K\)-theory

Keywords:

Kac-Moody algebra; equivariant K-group; combinatorial algebra; Weyl group

Citations:

Zbl 0426.55006; Zbl 0641.17008