11 papers
Relative Langlands duality and Koszul duality
Alexander Braverman, Michael Finkelberg, Roman Travkin
Consider a pair of -dual hyperspherical varieties and equipped with equivariant quantizations , . Assume…
Equivariant (-)homology of affine Grassmannian and Toda lattice
Roman Bezrukavnikov, Michael Finkelberg, Ivan MirkoviÄ
For an almost simple complex algebraic group with affine Grassmannian we consider the equivariant homology , and -theory $K^…
Mirabolic affine Grassmannian and character sheaves
Michael Finkelberg, Victor Ginzburg, Roman Travkin
We compute the Frobenius trace functions of mirabolic character sheaves defined over a finite field. The answer is given in terms of the character values of general linear groups o…
Modular reduction of complex representations of finite reductive groups
Roman Bezrukavnikov, Michael Finkelberg, David Kazhdan +1
The main result describes the Brauer-Nesbitt reduction of unipotent representations of a finite group of Lie type, expressing it as an explicit linear combination of the restrictio…
Relative Langlands duality for
Alexander Braverman, Michael Finkelberg, David Kazhdan +1
We establish an -duality converse to the one studied by the 1st, 2nd and 4th authors; this is also a case of a twisted version of the relative Langlands duality of Ben Zvi, Sake…
Equivariant Satake category and Kostant-Whittaker reduction
Roman Bezrukavnikov, Michael Finkelberg
We explain (following V. Drinfeld) how the equivariant derived category of the affine Grassmannian can be described in terms of coherent sheaves on the Langlands dual Lie algebra e…