arXiv subjects
Publications and source records attributed to M. Varagnolo.
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 affine Hecke algebras of type A. We also give some related results on the center of quiver Hecke algebras and cohomology of quiver varieties.
We study double affine Hecke algebras at roots of unity and their relations with deformed Hilbert schemes.
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 give several results concerning this functor.
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.
We classify finite dimensional simple spherical representations of rational double affine Hecke algebras, and we study a remarkable family of finite dimensional simple spherical representations of double affine Hecke algebras.
We prove the existence of canonical bases in the K-theory of quiver varieties. This existence was conjectured by Lusztig.
The fermionic Fock space admits two different actions of the quantized enveloping algebra of $\hat\sln$> The first one is a q-deformation of the well-known level-one representation of the affine Lie algebra and the second one is a new level-zero action arising from solvable lattices models. In this paper we prove that these two constructions can be glued together to get a representation of a new object: the toridal quantum group. This representation involves some difference operatorators. It is due to the fact that the specialization at q=1 of the toroidal algebra is isomorphic to the enveloping algebra of the universal central extension of a current algebra over a quantum torus.
The goal of the present paper is to prove with simple algebraic methods a Schur duality between Cherednik's double affine Hecke algebra of type GL(l) and the toroidal quantum group of type SL(n+1) introduced by V. Ginzburg, M. Kapranov and E. Vasserot in their "Langlands duality on algebraic surfaces".
Let R be a commutative ring, q a unit of R and P a multiplicatively antisymmetric matrix with coefficients which are integers powers of q. Denote by SE(q,P) the multiparameter quantum matrix bialgebra associated to q and P.Slightly generalizing [Hashimoto-Hayashi,Tohoku Math.Tohoku Math.J. 44(1992)],we define a multiparameter deformation $L_{ł/μ}V_P$ of the classical skew Schur module.In case R is a field and q is not a root of 1, arguments like those given in [H-H] show that $L_{ł/μ}V_P$ is irreducible and its decomposition into irreducibles is $\sum_νc(ł/μ;ν)L_νV_P$ where the coefficients are the usual Littlewood-Richardson ones. When R is any ring and q is allowed to be a root of 1, we construct a filtration of $L_{ł/μ}V_P$ as an SE(q,P)-comodule, such that its associated graded object is precisely $\sum_νc(ł/μ;ν)L_νV_P$.
We study the theory of representations of a multiparameter deformation of the function algebra of a simple algebraic group (as defined by Reshetikhin) when the quantum parameter is a root of unity. We extend the technics of De Concini-Lyubashenko in the standard quantum case.