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Springer theory via the Hitchin fibration

Published online by Cambridge University Press:  29 July 2011

David Nadler*
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA (email: [email protected])
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Abstract

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We develop the Springer theory of Weyl group representations in the language of symplectic topology. Given a semisimple complex group G, we describe a Lagrangian brane in the cotangent bundle of the adjoint quotient 𝔤/G that produces the perverse sheaves of Springer theory. The main technical tool is an analysis of the Fourier transform for constructible sheaves from the perspective of the Fukaya category. Our results can be viewed as a toy model of the quantization of Hitchin fibers in the geometric Langlands program.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2011

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