We give a classification of the graded simple modules cyclotomic quiver Hecke algebras type A using diagram calculus diagrammatic Cherednik algebra. also obtain non-trivial lower bound for dimension which is independent field characteristic.

These are notes for a talk in the MIT-Northeastern Spring 2015 Geometric Representation Theory Seminar. The main source is [G02]. We discuss baby Verma modules for rational Cherednik algebras at t = 0.

In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group G4. In particular, we classify the irreducible finite dimensional representations and compute their characters.

For certain negative rational numbers κ0, called singular values, and associated with the symmetric group SN on N objects, there exist homogeneous polynomials annihilated by each Dunkl operator when the parameter κ = κ0. It was shown by de Jeu, Opdam and the author (Trans. Amer. Math. Soc. 346 (1994), 237-256) that the singular values are exactly the values − n with 2 ≤ n ≤ N , m = 1, 2, . . . ...

We give a non-negative combinatorial formula, in terms of Littlewood-Richardson numbers, for the $$V^*$$ -homology unitary representations cyclotomic rational Cherednik algebra, and as consequence, graded Betti numbers ideals class subspace arrangements arising from reflection complex groups.