Related papers: CHAMP: A Cherednik Algebra Magma Package
During the 2004-2005 academic year the VIGRE algebra research group at the University of Georgia computed the complexities of certain Specht modules S^\lambda for the symmetric group, using the computer algebra program Magma. The complexity…
We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Cherednik algebras associated to the general and special…
We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group $G$ is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of $G$. We also provide a…
We develop a theory of weights for a quantum analogue of the symmetric pair (gl4,gl2 x gl2) realised as a quantum symmetric pair subalgebra. Based on Letzter's triangular decomposition we define Verma modules. Using magical operators that…
The Calogero-Moser families are partitions of the irreducible characters of a complex reflection group derived from the block structure of the corresponding restricted rational Cherednik algebra. It was conjectured by Martino in 2009 that…
We study the hyperplane arrangements associated, via the minimal model programme, to symplectic quotient singularities. We show that this hyperplane arrangement equals the arrangement of CM-hyperplanes coming from the representation theory…
We investigate rational $G$-modules $M$ for a linear algebraic group $G$ over an algebraically closed field $k$ of characteristic $p > 0$ using filtrations by sub-coalgebras of the coordinate algebra $k[G]$ of $G$. Even in the special case…
We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.
We construct a new class of algebras resembling enveloping algebras and generalizing orthogonal Gelfand-Zeitlin algebras and rational Galois algebras studied by [EMV,FuZ,RZ,Har]. The algebras are defined via a geometric realization in terms…
The rational Cherednik algebra $\HH$ is a certain algebra of differential-reflection operators attached to a complex reflection group $W$. Each irreducible representation $S^\lambda$ of $W$ corresponds to a standard module $M(\lambda)$ for…
Using combinatorial properties of complex reflection groups, we show that the generalised Calogero-Moser space associated to the centre of the corresponding rational Cherednik algebra is singular for all values of its deformation parameter…
We use homological perturbation machinery specific for the algebra category [P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications vol. 2, n. 5 (2000) 51-88] to give an algorithm for computing the…
The conformal Galilei algebra (CGA) is a non-semisimple Lie algebra labelled by two parameters $d$ and $\ell$. The aim of the present work is to investigate the lowest weight representations of CGA with $d = 1$ for any integer value of…
In this paper, a new construction of vertex algebras from more general vertex operators is given and a notion of quasi module for vertex algebras is introduced and studied. More specifically, a notion of quasi local subset(space) of $\Hom…
To every irreducible finite crystallographic reflection group (i.e., an irreducible finite reflection group G acting faithfully on an abelian variety X), we attach a family of classical and quantum integrable systems on X (with meromorphic…
It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…
We study Harish-Chandra bimodules over the rational Cherednik algebra $H_{c}(W)$ associated to a complex reflection group $W$ with parameter $c$. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We…
We give a classification of the graded simple modules of cyclotomic quiver Hecke algebras of type A using the diagram calculus of the diagrammatic Cherednik algebra. We also obtain a non-trivial lower bound for the dimension of the simple…
Given the spherical subalgebra $B$ of a rational Cherednik algebra, we aim to classify all finite groups $\Gamma$ for which there exists a domain $R$ on which $\Gamma$ acts by ring automorphisms, such that $B=R^{\Gamma}.$ We describe such…
The purpose of these notes is to provide the details of the Jacobian ring computations carried out in [1], based on the computer algebra system Magma [2].