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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Bases in equivariant $K$-theory
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by G. Lusztig PDF
Represent. Theory 2 (1998), 298-369 Request permission

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
  • 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