7 problems

Let $G$ be the finite reflection group associated with the Dunkl operators, let $k\geq 0$ be a multiplicity function, and let $K_G$ be the generalized exponential kernel defined by…

Let $K$ denote the Dunkl kernel associated with the multiplicity function $k$. For each $y\in\mathbb R^N$, consider the function $\xi\mapsto K(iy,\xi)$ on $\mathbb R^N$. Dunkl-kern…

Dunkl–de Jeu–Opdam conjecture. The two-part representations $(\mu,N-\mu)$ with $2\mu\geq N$ give rise to singular polynomials for the singular values

Let $R$ be a reflection group with a non-negative multiplicity function $k$, let $A_r$ be the Banach algebra of homogeneous polynomial series on the closed ball $B_r$, and let…

Macdonald–Mehta conjecture. The integral satisfies

Symmetry conjecture. This interval is always symmetric about $\kappa=0$.

Assume that the parameter $k$ is integral. Let $W$ be a complex reflection group, let $\operatorname{Irr}(W)$ denote its irreducible representations, and let … be the KZ twist indu…