# Non-vanishing of quantum geometric Whittaker coefficients

### APA

Bogdanova, E. (2024). Non-vanishing of quantum geometric Whittaker coefficients. Perimeter Institute. https://pirsa.org/24100074

### MLA

Bogdanova, Ekaterina. Non-vanishing of quantum geometric Whittaker coefficients. Perimeter Institute, Oct. 03, 2024, https://pirsa.org/24100074

### BibTex

@misc{ pirsa_PIRSA:24100074, doi = {10.48660/24100074}, url = {https://pirsa.org/24100074}, author = {Bogdanova, Ekaterina}, keywords = {Mathematical physics}, language = {en}, title = {Non-vanishing of quantum geometric Whittaker coefficients}, publisher = {Perimeter Institute}, year = {2024}, month = {oct}, note = {PIRSA:24100074 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

We will discuss the functor of geometric Whittaker coefficients in the context of quantum geometric Langlands. We will prove that tempered twisted D-modules on the stack of G-bundles on a smooth projective curve have non-vanishing Whittaker coefficients. Roughly, this means that a certain natural subcategory of twisted D-modules on the stack of G-bundles can be controlled by the category of twisted D-modules on the Beilinson-Drinfeld affine Grassmannian. The proof will combine generalizations of representation-theoretic and microlocal methods from the preceding works of Faergeman-Raskin and Nadler-Taylor respectively.