We establish a new simple explicit description of the Young diagram at each step combinatorial wall-crossing algorithm for rational Cherednik algebra applied to trivial representation. In this way we provide short and proof key theorem P. Dimakis G. Yue. also present conjecture on which was found using computer experiments.

We show that for Jack parameter α = −(k+1)/(r−1), certain Jack polynomials studied by Feigin–Jimbo–Miwa–Mukhin vanish to order r when k + 1 of the coordinates coincide. This result was conjectured by Bernevig and Haldane, who proposed that these Jack polynomials are model wavefunctions for fractional quantum Hall states. Special cases of these Jack polynomials include the wavefunctions of Laugh...

We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn o C`, the wreath product of the symmetric group and the cyclic group of order `, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size `. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The ...