102 citations · 259 across the 25 of their papers we have counts for
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Representations of shifted affine quantum groups and Coulomb branches
Michela Varagnolo, Eric Vasserot
We compare the integral category O of shifted affine quantum groups of symmetric and non symmetric types. To do so we compute the K-theoretic analog of the Coulomb branches with sy…
Non symmetric quantum loop groups and K-theory
Michela Varagnolo, Eric Vasserot
We realize the quantum loop groups and shifted quantum loop groups of arbitrary types, possibly non symmetric, using critical K-theory. This generalizes the Nakajima construction o…
Quantum loop groups and critical convolution algebras
Michela Varagnolo, Eric Vasserot
We realize geometrically a family of simple modules of (shifted) quantum loop groups including Kirillov-Reshetikhin and prefundamental representations. To do this, we introduce a n…
K-theoretic Hall algebras, quantum groups and super quantum groups
Michela Varagnolo, Eric Vasserot
We first prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum group. An essential step…
Coherent categorification of quantum loop algebras : the case
Peng Shan, Michela Varagnolo, Eric Vasserot
We construct an equivalence of graded Abelian categories from a category of representations of the quiver-Hecke algebra of type to the category of equivariant perverse…
Categorical actions on unipotent representations of finite classical groups
Olivier Dudas, Michela Varagnolo, Eric Vasserot
We review the categorical representation of a Kac-Moody algebra on unipotent representations of finite unitary groups in non-defining characteristic given by the authors. Then, we…
Categorical actions on unipotent representations I. Finite unitary groups
Olivier Dudas, Michela Varagnolo, Eric Vasserot
Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent representations of finite unitary groups in no…
On the center of quiver-Hecke algebras
P. Shan, M. Varagnolo, E. Vasserot
We compute the equivariant cohomology ring of the moduli space of framed instantons over the affine plane. It is a Rees algebra associated with the center of cyclotomic degenerate…
Categorifications and cyclotomic rational double affine Hecke algebras
Raphael Rouquier, Peng Shan, Michela Varagnolo +1
Varagnolo and Vasserot conjectured an equivalence between the category O for CRDAHA's and a subcategory of an affine parabolic category O of type A. We prove this conjecture. As ap…
Koszul duality of affine Kac-Moody algebras and cyclotomic rational DAHA
Peng Shan, Michela Varagnolo, Eric Vasserot
We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-Moody algebras. The main new tool is a relation between moment graphs and finite codimensi…
Canonical bases and affine Hecke algebras of type D
Peng Shan, Michela Varagnolo, Eric Vasserot
We prove a conjecture of Kashiwara and Miemietz on canonical bases and branching rules of affine Hecke algebras of type D. The proof is similar to the proof of the type B case.
Double affine Hecke algebras and affine flag manifolds, I
Michela Varagnolo, Eric Vasserot
This lecture reviews the classification of simple modules of double affine Hecke algebras via the K-theory of Steinberg varieties of affine type
Canonical bases and affine Hecke algebras of type B
Michela Varagnolo, Eric Vasserot
We prove a series of conjectures of Enomoto and Kashiwara on canonical bases and branching rules of affine Hecke algebras of type B. The main ingredient of the proof is a new grade…
Canonical bases and Khovanov-Lauda algebras
M. Varagnolo, E. Vasserot
We prove some recent conjectures of Khovanov-Lauda concerning the categorification of one-half of the quantum group associated with a simply laced Cartan datum.
Cyclotomic double affine Hecke algebras and affine parabolic category O, I
M. Varagnolo, E. Vasserot
Using the orbifold KZ connection we construct a functor from an affine parabolic category O of type A to the category O of a cyclotomic rational double affine Hecke algebra. We giv…
Finite dimensional representations of DAHA and affine Springers fibers : the spherical case
M. Varagnolo, E. Vasserot
We classify finite dimensional simple spherical representations of rational double affine Hecke algebras, and we study a remarkable family of finite dimensional simple spherical re…
Double affine Hecke algebras at roots of unity
M. Varagnolo, E. Vasserot
We study double affine Hecke algebras at roots of unity and their relations with deformed Hilbert schemes.
From double affine Hecke algebras to quantized affine Schur algebras
Michela Varagnolo, Eric Vasserot
We prove that the double affine Hecke algebra of type A is Morita equivalent to the quantized affine Schur algebra.
Periodic modules and quantum groups
Michela Varagnolo
We prove that the elements defined by Lusztig in a completion of the periodic module actually live in the periodic module, in the type A case. In order to prove this, we c…
Canonical bases and quiver varieties
M. Varagnolo, E. Vasserot
We prove the existence of canonical bases in the K-theory of quiver varieties. This existence was conjectured by Lusztig.