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Bases in equivariant $K$-theory

Author(s): G. Lusztig
Journal: Represent. Theory 2 (1998), 298-369.
MSC (1991): Primary 20G99
Posted: 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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Additional Information:

G. Lusztig
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

DOI: 10.1090/S1088-4165-98-00054-5
PII: S 1088-4165(98)00054-5
Received by editor(s): April 22, 1998
Received by editor(s) in revised form: June 16, 1998
Posted: August 19, 1998
Additional Notes: Supported in part by the National Science Foundation
Copyright of article: Copyright 1998, American Mathematical Society

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