Related papers: Representation type of level 1 KLR algebras $R^{\L…

We study the A_k generalized model of the O(1) loop model on a cylinder. The affine Hecke algebra associated with the model is characterized by a vanishing condition, the cylindric relation. We present two representations of the algebra:…

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…

Let G be a reductive group over a non-archimedean local field F. Consider an arbitrary Bernstein block Rep(G)^s in the category of complex smooth G-representations. In earlier work the author showed that there exists an affine Hecke algebra…

Let $\Lambda$ be a row-finite higher-rank graph with no sources. We identify a maximal commutative subalgebra $\mathcal{M}$ inside the Kumjian-Pask algebra ${\rm KP}_R(\Lambda)$. We also prove a generalized Cuntz-Krieger uniqueness theorem…

A Gelfand model for a semisimple algebra A over C is a complex linear representation that contains each irreducible representation of A with multiplicity exactly one. We give a method of constructing these models that works uniformly for a…

In this paper, we recover certain known results about the ladder representations of GL(n, Q_p) defined and studied by Lapid, Minguez, and Tadic. We work in the equivalent setting of graded Hecke algebra modules. Using the Arakawa-Suzuki…

We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in…

We show that every integral block of category O for the general linear Lie superalgebra is equivalent to a corresponding block of category O for the queer Lie superalgebra. This implies the truth of the Kazhdan-Lusztig conjecture for the…

We compute the K-groups of C^*-algebras arising from one-dimensional generalized solenoids. The results show that Ruelle algebras from one-dimensional generalized solenoids are one-dimensional generalizations of Cuntz-Krieger algebras.

It can be shown that it is possible to find a representation of Hecke algebras within Clifford algebras of multivectors. These Clifford algebras possess a unique gradation and a possibly non-symmetric bilinear form. Hecke algebra…

We develop a theory of vector valued automorphic forms associated to the Weil representation $\omega_f$ and corresponding to vector valued modular forms transforming with the ``finite'' Weil representation $\rho_L$. For each prime $p$ we…

We show that the category of representations of the Euclidean group of orientation-preserving isometries of two-dimensional Euclidean space is equivalent to the category of representations of the preprojective algebra of infinite type A. We…

A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with U_q(sl_2). We study its representation theory, and in particular, its category O.

We show that the Ariki-Terasoma-Yamada tensor module and its permutation submodules $ M(\lambda) $ are modules for the blob algebra when the Ariki-Koike algebra is a Hecke algebra of type $B$. We show that $ M(\lambda)$ and the standard…

In this monograph we undertake a comprehensive study of separable representations (as well as their unitary equivalence classes) of $C^*$-algebras associated to strongly connected finite $k$-graphs $\Lambda$. We begin with the…

We study the endomorphism algebras attached to Bernstein components of reductive $p$-adic groups and construct a local Langlands correspondence with the appropriate set of enhanced $L$-parameters, using certain "desiderata" properties for…

This paper describes a family of Hecke algebras H_\mu=End_G(Ind_U^G(\psi_\mu)), where U is the subgroup of unipotent upper-triangular matrices of G=GL_n(F_q) and \psi_\mu is a linear character of U. The main results combinatorially index a…

We explicitly compute the dimensions of certain idempotent truncations of RoCK blocks of cyclotomic quiver Hecke superalgebras. Equivalently, this amounts to a computation of the value of the Shapovalov form on certain explicit vectors in…

Let R: V x V -> V x V be a Hecke type solution of the quantum Yang-Baxter equation (a Hecke symmetry). Then, the Hilbert-Poincre' series of the associated R-exterior algebra of the space V is a ratio of two polynomials of degree m…

The aim of this paper is to gather and (try to) unify several approaches for the modular representation theory of Hecke algebras of type $B$. We attempt to explain the connections between Geck's cellular structures (coming from…