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AbstractWe develop the Springer theory of Weyl group representations in the language of symplectic topology. Given a semisimple complex groupG, we describe a Lagrangian brane in the cotangent bundle of the adjoint quotient 𝔤/Gthat 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 indoi:10.1112/s0010437x1100546x fatcat:lqqwl5sspbhjpfjfokms5c5naq