31 citations · 75 across the 21 of their papers we have counts for
22 papers
Iwahori Gaiotto conjecture for cotangent type
Roman Travkin, Ruotao Yang
We study the Iwahori Gaiotto conjecture for cotangent types and its application to the representation theory of the (mixed, small, and Lusztig) quantum supergroups. Using local and…
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…
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…
Gaiotto Conjecture for
Michael Finkelberg, Roman Travkin, Ruotao Yang
This paper is a part of the series proving the Gaiotto conjecture for basic classical quantum supergroups. The previous part arXiv:2107.02653 [math.RT] , arXiv:2306.09556 [math.RT]…
Lagrangian subvarieties of hyperspherical varieties
Michael Finkelberg, Victor Ginzburg, Roman Travkin
Given a hyperspherical -variety we consider the zero moment level of the action of a Borel subgroup . We conjecture…
Twisted Gaiotto equivalence for
Roman Travkin, Ruotao Yang
In , a series of subgroups indexed by were noticed by H. Jacquet-I. Piatetski Shapiro-J. Shalika, J. Cogdell, and D. Gaiotto. It was conjectured by D.…
The canonical global quantization of symplectic varieties in characteristic
Ekaterina Bogdanova, Dmitry Kubrak, Roman Travkin +1
Let be a smooth symplectic variety over a field of characteristic equipped with a restricted structure, which is a class whose d…
Orthosymplectic Satake equivalence, II
Alexander Braverman, Michael Finkelberg, Roman Travkin
This is a companion paper of arXiv:1909.11492 and arXiv:1912.01930. We prove an equivalence relating representations of a degenerate orthosymplectic supergroup with the category of…
Untwisted Gaiotto equivalence
Roman Travkin, Ruotao Yang
This is a successive paper of arXiv:1909.11492. We prove an equivalence between the category of finite-dimensional representations of degenerate supergroup an…
Coulomb branches of noncotangent type (with appendices by Gurbir Dhillon and Theo Johnson-Freyd)
Alexander Braverman, Gurbir Dhillon, Michael Finkelberg +2
We propose a construction of the Coulomb branch of a gauge theory corresponding to a choice of a connected reductive group and a symplectic finite-dimensio…
Gaiotto conjecture for
Alexander Braverman, Michael Finkelberg, Roman Travkin
We prove D.Gaiotto's conjecture about geometric Satake equivalence for quantum supergroup for generic . The equivalence goes through the category o…
A colimit presentation of via the Bott-Samelson hypercover
James Tao, Roman Travkin
Let be a semisimple, simply connected algebraic group over an algebraically closed field of characteristic zero. We prove that the -category of D-modules on the loop gr…
Homotopical presentations of braid groups via reduced lifts
James Tao, Roman Travkin
In 1997, Deligne showed that the reduced lift presentation of a finite type generalized braid group remains correct if it is (suitably) interpreted as a presentation of a topologic…
The affine Hecke category is a monoidal colimit
James Tao, Roman Travkin
Let be a semisimple simply-connected algebraic group over an algebraically closed field of characteristic zero. We prove that the affine Hecke category associated to the loop g…
Orthosymplectic Satake equivalence
Alexander Braverman, Michael Finkelberg, Roman Travkin
This is a companion paper of arXiv:1909.11492. We prove an equivalence relating representations of a degenerate orthosymplectic supergroup with the category of $SO(N-1,{\mathbb C}[…
Mirabolic Satake equivalence and supergroups
Alexander Braverman, Michael Finkelberg, Victor Ginzburg +1
We construct a mirabolic analogue of the geometric Satake equivalence. We also prove an equivalence that relates representations of a supergroup with the category of $GL(N-1,{\math…
Moduli spaces, indecomposable objects and potentials over a finite field
Galyna Dobrovolska, Victor Ginzburg, Roman Travkin
Given a linear category over a finite field such that the moduli space of its objects is a smooth Artin stack (and some additional conditions) we give formulas for an exponential s…
Resolutions with conical slices and descent for the Brauer group classes of certain central reductions of differential operators in characteristic
Dmitry Kubrak, Roman Travkin
For a smooth variety over an algebraically closed field of characteristic , to a differential 1-form on the Frobenius twist one can associate an Azumaya algebr…
Quantization of Hitchin integrable system via positive characteristic
Roman Bezrukavnikov, Roman Travkin, Tsao-Hsien Chen +1
In a celebrated unpublished manuscript Beilinson and Drinfeld quantize the Hitchin integrable system by showing that the global sections of critically twisted differential operator…
Quantum geometric Langlands correspondence in positive characteristic: the GL(N) case
Roman Travkin
We prove a version of quantum geometric Langlands conjecture in characteristic . Namely, we construct an equivalence of certain localizations of derived categories of twisted cr…
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…
Mirabolic Robinson-Schensted-Knuth correspondence
Roman Travkin
The set of orbits of in is finite, and is parametrized by the set of certain decorated permutations in a work of Solomon. We describe a Miraboli…