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Working paper

Gaiotto-Witten superpotential and Whittaker D-modules on monopoles

Braverman A., Dobrovolska G., Michael Finkelberg.
Let G be an almost simple simply connected group over complex numbers. For a positive element α of the coroot lattice of G let Z^α denote the space of based maps from the projective line to the flag variety of G of degree α. This space is known to be isomorphic to the space of framed euclidean G-monopoles with maximal symmetry breaking at infinity of charge α. In [Finkelberg-Kuznetsov-Markarian-Mirkovi\'c] a system of (\'etale, rational) coordinates on Z^α is introduced. In this note we compute various known structures on Z^α in terms of the above coordinates. As a byproduct we give a natural interpretation of the Gaiotto-Witten superpotential and relate it to the theory of Whittaker D-modules introduced by D.Gaitsgory.