Bases in equivariant 𝐾-theory

Lusztig, G.

doi:10.1090/S1088-4165-98-00054-5

Bases in equivariant $K$-theory
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by G. Lusztig

Represent. Theory 2 (1998), 298-369

DOI: https://doi.org/10.1090/S1088-4165-98-00054-5

Published electronically: August 19, 1998

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Abstract:

In this paper we construct a canonical basis for the equivariant $K$-theory of the flag manifold of a semisimple simply connected $\mathbf {C}$-algebraic group with respect to the action of a maximal torus times $\mathbf {C}^{*}$. 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.

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