4.6 Article

Chiral principal series categories I: Finite dimensional calculations

Journal

ADVANCES IN MATHEMATICS
Volume 388, Issue -, Pages -

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2021.107856

Keywords

Geometric Langlands; Whittaker; Zastava space

Categories

Funding

  1. National Science Foundation [1402003]
  2. Direct For Mathematical & Physical Scien
  3. Division Of Mathematical Sciences [1402003] Funding Source: National Science Foundation

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This paper initiates a study of D-modules on the FeiginFrenkel semi-infinite flag variety using the Beilinson-Drinfeld factorization theory. By calculating Whittaker-twisted cohomology groups of Zastava spaces, certain finite-dimensional subvarieties of the affine Grassmannian, it is shown that these cohomology groups realize the nilradical of a Borel subalgebra for the Langlands dual group in a precise sense. This geometric realization of the Langlands dual group is compared to the standard one provided by (factorizable) geometric Satake.
This paper begins a series studying D-modules on the FeiginFrenkel semi-infinite flag variety from the perspective of the Beilinson-Drinfeld factorization (or chiral) theory. Here we calculate Whittaker-twisted cohomology groups of Zastava spaces, which are certain finite-dimensional subvarieties of the affine Grassmannian. We show that such cohomology groups realize the nilradical of a Borel subalgebra for the Langlands dual group in a precise sense, following earlier work of Feigin-Finkelberg-Kuznetsov-Mirkovic and BravermanGaitsgory. Moreover, we compare this geometric realization of the Langlands dual group to the standard one provided by (factorizable) geometric Satake. (c) 2021 Published by Elsevier Inc.

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