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Bases in equivariant \(K\)-theory. (English) Zbl 0901.20034
Summary: We construct a canonical basis for the equivariant \(K\)-theory of the flag manifold of a semisimple simply connected \(\mathbb{C}\)-algebraic group with respect to the action of a maximal torus times \(\mathbb{C}^*\). We relate this basis to the canonical basis of the “periodic module” for the affine Hecke algebra. The construction admits a (conjectural) generalization to the case where the flag manifold is replaced by the zero set of a nilpotent vector field.

MSC:
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
14M15 Grassmannians, Schubert varieties, flag manifolds
20G05 Representation theory for linear algebraic groups
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
14M30 Supervarieties
20C08 Hecke algebras and their representations
19L47 Equivariant \(K\)-theory
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