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arXiv · 2611.08464

Symplectic singularities in Relative Langlands duality for products of general linear groups

Bruno da Silveira Dias·Victor Ginzburg
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Abstract

It was shown by Braverman-Finkelberg-Nakajima that the regular perverse sheaf on the affine Grassmannian of type A is isomorphic to the ring object associated to a Gelfand-Tsetlin quiver. We use this result to identify, for any finite dimensional representation $\mathbf{N}$ of a product of general linear groups, the relative Langlands dual $(T^*\mathbf{N})^\vee$ of $T^*\mathbf{N}$ with the Coulomb branch of a suitable representation. By a result of Bellamy, this implies that $(T^*\mathbf{N})^\vee$ has symplectic singularities.

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Bruno da Silveira Dias, Victor Ginzburg. 2026-11-05. Symplectic singularities in Relative Langlands duality for products of general linear groups. https://arxiv.org/abs/2611.08464

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