1.1 Whittaker and Bessel models are of importance in the theory of automorphic representations of GSp4. This paper is the first in a series of two, where we study some phenomena corresponding to these models in the geometric Langlands program. The theory of Whittaker functors for GLn is an essential technical tool in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langl...

This paper is intended as an introduction to the gauge theory approach [15] to the geometric Langlands correspondence. But, rather than a conventional overview, which I have attempted elsewhere [25, 26], the focus here is on understanding a very particular result, which I learned of from [13]. (Another standard reference on closely related matters is [17].) This introduction is devoted to descr...

Introduction 2 1. Harmonic analysis and unitary duals 2 2. Non-discrete locally compact fields, classical groups, reductive groups 4 3. K0-finite vectors 7 4. Smooth representations 8 5. Parabolically induced representations 9 6. Jacquet modules 12 7. Filtrations of Jacquet modules 14 8. Square integrable and tempered representations 15 9. Langlands classification 16 10. Geometric lemma and alg...

Let X be a smooth projective curve over an algebraically closed field of characteristic > 2. Consider the dual pair H = GO2m, G = GSp2n over X , where H splits over an étale two-sheeted covering π : X̃ → X . Write BunG and BunH for the stacks of G-torsors and H-torsors on X . We show that for m ≤ n (respectively, for m > n) the theta-lifting functor FG : D(BunH) → D(BunG) (respectively, FH : D(B...