17 problems

Let $G$ be a finite reflection group acting on $\mathbb R^q$, let $k\geq0$ be a multiplicity function, let $J_k$ be the associated $G$-invariant generalized Bessel function, and le…

Let a root system be given with non-negative multiplicities, and let the associated Dunkl-type Bessel functions be defined on the underlying Weyl chamber. Positive product formula…

Existence conjecture. It is conjectured that there exists a commutative hypergroup on $C$ whose multiplicative functions include the functions $J_k(\,\cdot\,,y)$ for all…

Hypergroup conjecture. For arbitrary reflection groups and non-negative multiplicities, this convolution should make $\overline C$ into a commutative hypergroup. In the special cas…

Let $R$ be a root system with reflection group $G$, Weyl chamber $C$, and generalized Bessel function $J_k$ associated with a multiplicity function $k$. For $x,y\in\overline C$, su…

Let $(\mathcal{A},U,\Omega)$ be a Poincaré covariant net of local observables, and let $\operatorname*{QuOp}(\mathcal{A})$ denote its quantum operations. In the 3+1-dimensional con…

Let $X$ be a commutative hypergroup. An exponential monomial is an exponential polynomial associated with an exponential $m$ on $X$, and its variety is the finite-dimensional varie…

Let $\Gamma$ be a graph and $v_0$ a vertex of $\Gamma$. Call $(\Gamma,v_0)$ hypergroup productive if a random walk on $\Gamma$ starting from $v_0$ produces a discrete hypergroup. S…

Let $(\Gamma,w_0)$ be a pointed graph satisfying the conditions $(S1)$ and $(S2)$. Say that it produces a hypergroup when its associated distance distribution yields a hypergroup.…

Conjecture on Morita-equivalent extensions. $\widetilde{\mathcal{F}}$ is a $K$-graded extension of $\widetilde{\mathcal{G}}$.

Conjecture on charged intertwiners. The action on the charged intertwiners $\{\psi_{\rho,i}\}$ in Xu's construction essentially coincides with

Let $L$ be a hypergroup with an exponential family, and let sine functions on $L$ be defined relative to the exponentials in that family. The exponential-family sine-function conje…

Partial-QFT and quadratic-phase simulation conjecture. There exist nontrivial families of abelian hypergroups for which the normalizer circuits of the paper's simulation theorem re…

Extension conjecture. The simulation result can be extended to all normalizer gates, despite the non-monomiality and non-unitarity issues of hypergroup Pauli operators.

Let $P_+$ be the index set of Jacobi polynomials $R_\lambda^p$, and define the linearization coefficients $c_{\lambda,\mu,\tau}$ by … For integer $p\geq q$, these coefficients are…

Amenability–Haar measure boundedness conjecture. For the $d$-variable Chebychev polynomial hypergroups, the hypergroup algebra is amenable if and only if the Haar measure is bounde…

Let $p\ge 2q-1$. The hypergroup $(C_q\times\mathbb R,*_p)$ has continuous multiplicative functions $\psi_{\lambda,l}^p$ for $\lambda\in\mathbb C^q$ and $l\in\mathbb C$. Parametriza…