Related papers: Scattering matrices and affine Hecke algebras

We generalize the geometric construction of quiver Hecke algebras from Varagnolo and Vasserot to a setup with arbitrary connected reductive groups. This corresponds to replacing quiver representations by generalized quiver representations…

Scattering diagrams arose in the context of mirror symmetry, but a special class of scattering diagrams (the cluster scattering diagrams) were recently developed to prove key structural results on cluster algebras. We use the connection to…

In this paper, we prove classical affine W-algebras associated to Lie superalgebras (W-superalgebras) can be constructed in two different ways: via affine classical Hamiltonian reductions and via taking quasi-classical limits of quantum…

For a general affine Hecke algebra H we study its Schwartz completion S. The main theorem is an exact description of the image of S under the Fourier isomorphism. An important ingredient in the proof of this result is the definition and…

We construct highest-weight modules and a Yangian extension of the centrally extended sl(1|1)^2 superalgebra, that is a symmetry of the worldsheet scattering associated with the AdS3/CFT3 duality. We demonstrate that the R-matrix…

We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra, thus obtaining an "affine" version of the construction of [14]. Explicitly, we show that the aforementioned trace is generated by the objects…

This paper is a following to math.RT/0410454. For a finite group of Lie type we study the endomorphisms, commuting with the group action, of a Deligne-Lusztig variety associated to a regular element of the Weyl group. We state some general…

The commutative trigonometric shuffle algebra ${\mathrm A}$ is a space of symmetric rational functions satisfying certain wheel conditions. We describe a ring isomorphism between ${\mathrm A}$ and the center of the Hecke algebra using a…

We construct a non-trivial homomorphism from the Guay's affine Yangian to the universal enveloping algebra of non-rectangular $W$-algebras of type $A$. In order to construct the homomorphism, we extend the Guay's affine Yangian and its…

We compute the center and the Lie algebra of outer derivations of a familiy of algebras of differential operators associated to hyperplane arrangements of the affine space A 3. The results are completed for 4-braid arrangements and for…

We briefly summarize our systematic construction procedure of q-deforming maps for Lie group covariant Weyl or Clifford algebras.

The orbits of Weyl groups W(A(n)) of simple A(n) type Lie algebras are reduced to the union of orbits of the Weyl groups of maximal reductive subalgebras of A(n). Matrices transforming points of the orbits of W(An) into points of subalgebra…

Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter…

Affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of Robinson-Schensted correspondence. We show that AMBC gives a simple way to compute a distinguished…

The Kac-Moody affine Hecke algebra $\mathcal{H}$ was first constructed as the Iwahori-Hecke algebra of a $p$-adic Kac-Moody group by work of Braverman, Kazhdan, and Patnaik, and by work of Bardy-Panse, Gaussent, and Rousseau. Since…

We introduce a generalized version of a q-Schur algebra (of parabolic type) for arbitrary Hecke algebras over extended Weyl groups. We describe how the decomposition matrix of a finite group with split BN-pair, with respect to a…

In this paper we propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. We conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on…

We give a concrete description of the category of etale algebras over the ring of Witt vectors of a given finite length with entries in an arbitrary ring. We do this not only for the classical p-typical and big Witt vector functors but also…

We compute the centre of the cyclotomic Hecke algebra attached to $G(m,1,2)$ and show that if $q \neq 1$ it is equal to the image of the centre of the affine Hecke algebra $\Ha$. We also briefly discuss what is known about the relation…

Random walk on the chambers of hyperplanes arrangements is used to define a family of card shuffling measures $H_{W,x}$ for a finite Coxeter group W and real $x \neq 0$. By algebraic group theory, there is a map from the semisimple orbits…