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arXiv · 2603.23435

Exponential motives on the affine Grassmannian

Robert Cass·Thibaud van den Hove·Jakob Scholbach
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Abstract

We develop a notion of exponential motives on general prestacks equipped with a $\mathbf{G}_a$-action, and compare them with Whittaker motives via Gaitsgory's Kirillov model. We then establish foundational results for exponential motives on affine flag varieties concerning Tate motives and t-structures. We use this to prove a motivic Casselman-Shalika equivalence, relating exponential Tate motives on the affine Grassmannian to ind-coherent sheaves on the classifying stack of the Langlands dual group. The decategorification of this equivalence provides a new construction of the Whittaker module for the spherical Hecke algebra which works for arbitrary coefficients, including a generic version.

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Robert Cass, Thibaud van den Hove, Jakob Scholbach. 2026-03-24. Exponential motives on the affine Grassmannian. https://arxiv.org/abs/2603.23435

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