Related papers: Introduction to double Hecke algebras

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a…

We construct an action of the graded double affine Hecke algebra (DAHA) on the parabolic Hitchin complex, extending the affine Weyl group action constructed in \cite{GSI}. In particular, we get representations of the degenerate DAHA on the…

In this paper, we define a number of closely related isomorphisms. On one side of these isomorphisms sit a number of of algebras generalizing the Hecke and affine Hecke algebras, which we call the "Hecke family"; on the other, we find…

Assume that $\mathbb F$ is an algebraically closed field and let $q$ denote a nonzero scalar in $\mathbb F$ that is not a root of unity. The universal DAHA (double affine Hecke algebra) $\mathfrak H_q$ of type $(C_1^\vee,C_1)$ is a unital…

We give a $K$-theoretic realization of all affine Hecke algebras with two unequal parameters including exceptional types. This extends the celebrated work of Kazhdan and Lusztig, who gave a $K$-theoretic realization of affine Hecke algebras…

We generalize quantum Drinfeld Hecke algebras by incorporating a 2-cocycle on the associated finite group. We identify these algebras as specializations of deformations of twisted skew group algebras, giving an explicit connection to…

An enhanced algebraic group $\uG$ of $G=\GL(V)$ over $\bbc$ is a product variety $\GL(V)\times V$, endowed with an enhanced cross product. Associated with a natural tensor representation of $\uG$, there are naturally Levi and parabolic…

For the rational Baker-Akhiezer functions associated with special arrangements of hyperplanes with multiplicities we establish an integral identity, which may be viewed as a generalisation of the self-duality property of the usual Gaussian…

We introduce a new language to describe the geometry of affine Deligne-Lusztig varieties in affine flag varieties. This second part of a two paper series uses this new language, i.e. the double Bruhat graph, to describe certain structure…

A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace-Dunkl operator associated to the $\mathbb{Z}_2^n$ root system. This algebra is also the invariance algebra of the generic…

In this work, we study multiplicity-free induced representations of finite groups. We analyze in great detail the structure of the Hecke algebra corresponding to the commutant of an induced representation and then specialize to the…

We construct an algebra that is an elliptic generalization of $A_1$ spherical DAHA acting on its finite-dimensional module at $t=-q^{-K/2}$ with $K=2$. We prove that $PSL(2,\mathbb Z)$ acts by automorphisms of the algebra we constructed,…

We consider the algebra of Hecke correspondences (elementary transformations at a single point) acting on the algebraic K-theory groups of the moduli spaces of stable sheaves on a smooth projective surface S. We derive quadratic relations…

As a sequel to [14], in this article we first introduce a so-called duplex Hecke algebras of type B which is a Q(q)-algebra associated with the Weyl group W (B) of type B, and symmetric groups S_l for l = 0, 1, . . . ,m, satisfying some…

We derive a canonical analysis of a double null 2+2 Hamiltonian description of General Relativity in terms of complex self-dual 2-forms and the associated SO(3) connection variables. The algebra of first class constraints is obtained and…

In this work, we introduce Urod algebras associated to simply-laced Lie algebras as well as the concept of translation of W-algebras. Both results are achieved by showing that the quantum Hamiltonian reduction commutes with tensoring with…

Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a…

This paper investigates the connections between buildings and Hecke algebras through the combinatorial study of two algebras spanned by averaging operators on buildings. As a consequence we obtain a geometric and combinatorial description…

We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…

We propose a generalization of the level-rank dualities arising from Uglov's work on higher-level Fock spaces. The statements use Hecke algebras defined by Brou\'{e}-Malle, which conjecturally describe the endomorphisms of Lusztig induction…