Related papers: Interpolating between promotion and the long cycle

Let $W$ be an affine Weyl group, and let $\Bbbk$ be a field of characteristic $p>0$. The diagrammatic Hecke category $\mathcal{D}$ for $W$ over $\Bbbk$ is a categorification of the Hecke algebra for $W$ with rich connections to modular…

In this paper we extend the results in [Ra] on the representation of the Hecke algebra, determined by the matrix coefficients of a projective, unitary representation, in the discrete series of representations of the ambient group, to a more…

Previously we gave a conjectural cohomological argument for the validity of the Riemann hypotheses for Hasse-Weil zeta functions. In the present note we sketch how the same cohomological formalism would imply the conjectured positivity…

We construct a large class of examples of the cyclic sieving phenomenon by expoiting the representation theory of semi-simple Lie algebras. Let $M$ be a finite dimensional representation of a semi-simple Lie algebra and let $B$ be the…

Schutzenberger's promotion operator, pro, is a fundamental map in dynamical algebraic combinatorics. At first, its action was mainly considered on standard Young tableaux. But pro was subsequently shown to have interesting properties when…

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

We introduce and study some affine Hecke algebras of type ADE, generalising the affine Hecke algebras of GL. We construct irreducible calibrated representations and describe the calibrated spectrum. This is done in terms of new families of…

We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.

The main aim of the paper is to formulate and prove a result about the structure of double affine Hecke algebras which allows its two commutative subalgebras to play a symmetric role. This result is essential for the theory of intertwiners…

This paper constructs a representation of a Hecke algebra on a vector space spanned by the involutions in a Coxeter group.

We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by…

We study the reduction modulo $l$ of some elliptic representations; for each of these representations, we give a particular lattice naturally obtained by parabolic induction in giving the graph of extensions between its irreducible…

We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain…

We prove in the vector-valued spaces $L^2(\mathbb{R}_+, X)$ (where $X$ is a finite dimensional Hilbert space) the cyclicity for the semi-group of left translations of some particular functions with support included in a lacunary system of…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

The paper offers versions of Hilbert's Irreducibility Theorem for the lifting of points in a cyclic subgroup of an algebraic group to a ramified cover. A version of Bertini Theorem in this context is also obtained.

In this paper, we establish connections between the first extensions of simple modules and certain filtrations of of standard modules in the setting of graded Hecke algebras. The filtrations involved are radical filtrations and Jantzen…

We show how to derive new instances of the cyclic sieving phenomenon from old ones via elementary representation theory. Examples are given involving objects such as words, parking functions, finite fields, and graphs.

In this note we are interested in labelling the irreducible representations of non-semisimple specialisations of Hecke algebras of complex reflection groups. We will use category O for the rational Cherednik algebra and the KZ functor…

Let T_k denote the Hecke algebra acting on newforms of weight k and level N. We prove that the power of p dividing the index of T_k inside its normalisation grows at least linearly with k (for fixed N), answering a question of Serre. We…