PIRSA:24100074 Scientific Series Mathematical physics

DOI10.48660/24100074

Series: Mathematical Physics

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

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

@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}}
}

Abstract

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.

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