Related papers: Restricted rational Cherednik algebras
The survey of the current state of the theory of Krichever-Novikov algebras including new results on local central extensions, invariants, representations and casimir operators.
Braided doubles provide a unifying framework for classical and quantum universal enveloping algebras and rational Cherednik algebras. They are a class of algebras with triangular decomposition, arising from a deformation problem, the…
We describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed quantum-mechanical problems have a Fock-space…
We study relative Cohn path algebras, also known as Leavitt-Cohn path algebras, and we realize them as partial skew group rings (to do this we prove uniqueness theorems for relative Cohn path algebras). Furthermore, given any graph $E$ we…
It is well-known that a quiver Q of type A_n is representation-finite, and that its indecomposable representations are thin (all Jordan-Hoelder multiplicities are 0 or 1). By now, various methods of proof are known. The aim of this note is…
In this paper, we show that the class of representable residuated semigroups has the finite representation property. That is, every finite representable residuated semigroup is isomorphic to some algebra over a finite base. This result…
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…
We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a…
We consider quiver representations respecting a quiver automorphism and show that the dimension vectors of the indecomposables are precisely the positive roots of an associated symmetrisable Kac-Moody Lie algebra. Moreover, every such Lie…
Drinfeld orbifold algebras deform skew group algebras in polynomial degree at most one and hence encompass graded Hecke algebras, and in particular symplectic reflection algebras and rational Cherednik algebras. We introduce parametrized…
Let k be a field. A finite dimensional k-algebra is said to be minimal representation-infinite provided it is representation-infinite and all its proper factor algebras are representation-finite. Our aim is to classify the special biserial…
We define Lie subalgebras of the group algebra of a finite pseudo-reflection group that are involved in the definition of the Cherednik KZ-systems, and determine their structure. We provide applications for computing the Zariski closure of…
This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated…
We introduce the notion of ``finite general representation type'' for a finite-dimensional algebra, a property related to the ``dense orbit property'' introduced by Chindris-Kinser-Weyman. We use an interplay of geometric, combinatorial,…
We consider the quantum-mechanical algebra of observables generated by canonical quantization of $SL(2,R)$ Chern-Simons theory with rational charge on a space manifold with torus topology. We produce modular representations generalizing the…
In this paper, we shall establish the Mackey formulas in the following two set ups: (i) on the tensor induction and restriction functors on the modules over cyclotomic Hecke algebras (Ariki-Koike algebras) and their standard subalgebras of…
In this paper we consider two problems relating to the representation theory of Lie algebras ${\mathfrak g}$ of reductive algebraic groups $G$ over algebraically closed fields ${\mathbb K}$ of positive characteristic $p>0$. First, we…
The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero-Moser systems. In the special case of symmetric pair g=gl(n,2m),…
Multidimensional contractions of irreducible representations of the Cayley-Klein unitary algebras in the Gel'fand-Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…