We classify the irreducible unitary modules in category O c for the rational Cherednik
algebras of type G (r, 1, n) and give explicit combinatorial formulas for their graded …

For a finite dimensional representation V of a finite reflection group W, we consider the
rational Cherednik algebra H t, c (V, W) associated with (V, W) at the parameters t≠ 0 and c …

We present recent joint work with Peter Trapa on the notion of twisted Dirac index and its
applications to (twisted) characters and to extensions of modules in a short and informal …

We construct characteristic-free bases and BGG resolutions of unitary simple modules of
quiver Hecke algebras and Cherednik algebras. We hence solve and vastly generalise …

In this paper, we study a compact analogue of Schur-Weyl duality for real orthogonal and
symplectic groups. We analyse the functors F μ, k defined in [12], and introduce a new …

We give a non-negative combinatorial formula, in terms of Littlewood-Richardson numbers,
for the V^* V∗-homology of the unitary representations of the cyclotomic rational Cherednik …

We define a family of Dirac operators for the Dunkl angular momentum algebra depending
on certain central elements of the group algebra of the Pin cover of the Weyl group inherent …

We consider the deformed versions of the classical Howe dual pairs (O (r, C), sl (2, C)) and
(O (r, C), spo (2| 2, C)) in the context of a rational Cherednik algebra H c= H c (W, h) …

The aim of this paper is to define cubic Dirac operators for colour Lie algebras. We give a
necessary and sufficient condition to construct a colour Lie algebra from an ϵ-orthogonal …

We derive an explicit description of the genuine projective representations of the symmetric
group S n using Dirac cohomology and the branching graph for the irreducible genuine …