Related papers: Representation type of level 1 KLR algebras $R^{\L…
These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…
Let $L$ be a Lie algebra of Block type over $\C$ with basis $\{L_{\alpha,i}\,|\,\alpha,i\in\Z\}$ and brackets $[L_{\alpha,i},L_{\beta,j}]=(\beta(i+1)-\alpha(j+1))L_{\alpha+\beta,i+j}$. In this paper, we shall construct a formal distribution…
Schocker classified the representation type of the descent algebra of type $\mathbb{A}$ over any field of characteristic zero. In an earlier paper, the authors extended this classification for type $\mathbb{A}$ to fields of positive…
Let $n\in\mathbb{N}$ and $K$ be any field. For any symmetric generalized Cartan matrix $A$, any $\beta$ in the positive root lattice with height $n$ and any integral dominant weight $\Lambda$, one can associate a quiver Hecke algebras…
Homology theories categorifying quantum group link invariants are known to be governed by the representation theory of quiver Hecke algebras, also called KLRW algebras. Here we show that certain cylindrical KLRW algebras, relevant in…
This paper surveys the representation theory of rational Cherednik algebras. We also discuss the representations of the spherical subalgebras. We describe in particular the results on category O. For type A, we explain relations with the…
Based on a recent result of Mathas and the author, we prove that Uno's conjecture on representation types of Hecke algebras is true for all Hecke algebras of classical type.
Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke algebra…
In this paper, we define a quotient of the cyclotomic Hecke algebra of type $G(r,1,n)$ as a generalisation of the Temperley-Lieb algebras of type $A$ and $B$. We establish a graded cellular structure for the generalised Temperley-Lieb…
The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie…
We investigate the representation theory of the rational and trigonometric Cherednik algebra of type $GL_n$ by means of combinatorics on periodic (or cylindrical) skew diagrams. We introduce and study standard tableaux and plane partitions…
This paper classifies the blocks of the cyclotomic Hecke algebras of type G(r,1,n) over an arbitrary field. Rather than working with the Hecke algebras directly we work instead with the cyclotomic Schur algebras. The advantage of these…
We prove that cyclotomic Yokonuma--Hecke algebras of type A are cyclotomic quiver Hecke algebras and we give an explicit isomorphism with its inverse, using a similar result of Brundan and Kleshchev on cyclotomic Hecke algebras. The quiver…
We prove that the KLR algebra associated with the cyclic quiver of length $e$ is a subquotient of the KLR algebra associated with the cyclic quiver of length $e+1$. We also give a geometric interpretation of this fact. This result has an…
We build representations of the affine and double affine braid groups and Hecke algebras of type $C^\vee C_n$, based upon the theory of quantum symmetric pairs $(U,B)$. In the case $U=U_q(gl_N)$, our constructions provide a quantization of…
This paper is a survey on the representation theory of Hecke algebras, Ariki-Koike algebras and connections with quantum group.
We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a…
This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced…
We develop the homological theory of KLR algebras of symmetric affine type. For each PBW basis, a family of standard modules is constructed which categorifies the PBW basis.
We construct a level $-\frac{1}{2}$ vertex representation of the quantum N-toroidal algebra for type $C_n$, which is a natural generalization of the usual quantum toroidal algebra. The construction also provides a vertex representation of…