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Metaplectic Whittaker Functions and Quantum Groups at Roots of Unity

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NC2W02 - Crossing the bridge: New connections in number theory and physics

We will explain a connection between Whittaker functions on an n-fold metaplectic cover of a group G (over the p-adics) and representations of a quantum group at an n-th root of unity attached to the Langlands dual of G. Our construction involves the introduction of some new Kazhdan-Lusztig type polynomials twisted by Gauss sums, and suggests two natural candidates for what might be called a geometric Casselman-Shalika formula for covering groups.  Joint work in progress with Valentin Buciumas.

This talk is part of the Isaac Newton Institute Seminar Series series.

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