## 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 âperiodic moduleâ 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.## References

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## Bibliographic Information

**G. Lusztig**- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Received by editor(s): April 22, 1998
- Received by editor(s) in revised form: June 16, 1998
- Published electronically: August 19, 1998
- Additional Notes: Supported in part by the National Science Foundation
- © Copyright 1998 American Mathematical Society
- Journal: Represent. Theory
**2**(1998), 298-369 - MSC (1991): Primary 20G99
- DOI: https://doi.org/10.1090/S1088-4165-98-00054-5
- MathSciNet review: 1637973