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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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