5 problems

Let $I$ be the set of Dynkin labels, let $I_<\subset I$ be the labels of the short roots in types $B_N$ and $C_N$, and let $t_a=2$ for $a\in I_<$ and $t_a=1$ otherwise. Let…

For a classical root system of type $D_N$, $B_N$, or $C_N$, let $M_{a,k}^{(G)}$ be the corresponding difference operators and let $\Pi_\lambda^{(G)}(q^{-1};\mathbf{x})$ be the dual…

Let $G$ be one of the classical types $D_N$, $B_N$, or $C_N$, and let $M_{a,n}^{(G)}$ be the associated Macdonald difference operators, with the superscript $G$ omitted below. Let…

Let $L$ be an irreducible differential operator of order $k$ solving the generalized Bochner–Krall problem, and let $\Lambda$ be its corresponding difference operator. Order-preser…

Brändén–Krasikov–Shapiro conjecture. The operator $T$ preserves the set of real-rooted polynomials of degree at most $m$ whose mesh is at least $1$ if and only if $T((x)_m)$ is rea…