7 problems

Graczyk–Sawyer sharpness conjecture. The number $n+1$ is sharp for the property that every convolution product of $n+1$ continuous $K$-bi-invariant measures on $G$ is absolutely co…

Let $k$ indistinguishable bosons have $G={\rm SU}(N)$ with $N={{n+k-1}\choose{k}}$, and let $k$ indistinguishable fermions have $G={\rm SU}(K)$ with $K={{n}\choose{k}}$. In both ca…

Let $C_n$ and $D_n$ denote the classical compact Lie groups of types $C$ and $D$. For an element $x$ in one of these groups, let $S_x$ be defined from its dominant type, and call a…

Let $R_n$ and $\widehat R_n$ be the polynomials whose coefficients are denoted by $r_\kappa$ and $\hat r_\kappa$, respectively. Nonnegativity conjecture. The coefficients…

Exceptional-pair conjecture. The convolution

Let $U/K$ be a compact symmetric space, let $a\in U$ be outside the normalizer $N_U(K)$ of $K$ in $U$, and let $\mu_a$ be the normalized singular measure supported on the double co…

Gupta–Hare's $L^{2}$ conjecture. The Radon–Nikodym derivative