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.

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.