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
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Funding
- National Science Foundation [1402003]
- Direct For Mathematical & Physical Scien
- 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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