34 problems

Let $\mathfrak{g}$ be a real compact Lie algebra, and replace the operators and relations in Theorem … holds for all real compact Lie algebras. The theorem for $\mathfrak{su}(2)$ e…

Let $\mathfrak{h}$ be the Cartan subalgebra and let $\Lambda$ denote the set of parameters for which the corresponding quantization exists, viewed as a semigroup under the semigrou…

Let $\mathcal{M}^{G}$ be the moduli space associated with a simple group $G$, and let the star product be the product defined by equation on the chord-diagram algebra. Descent conj…

Let $B$ be a local commutative algebra over $k$ with maximal ideal ${\mathfrak m} \subset B$, and let $\widetilde{A}$ be a flat associative algebra over $B$ such that…

Existence conjecture. Any modified dynamical $r$-matrix admits a formal twist quantization.

Let ${\mathfrak b}$ be a finite-dimensional basic algebra, and let ${\mathfrak n}({\mathfrak b})$ be its Lie normalizer in $P({\mathfrak b})$. Strong quantization conjecture. Every…

Let $M$ be a symplectic manifold and ${\mathfrak b}$ a basic algebra such that $P^1({\mathfrak b})$ is dense in $C^{\infty}(M)$, where $P^1({\mathfrak b})$ denotes the polynomial a…

Let $M$ be a symplectic manifold with a finite-dimensional basic algebra ${\mathfrak b}$. Let $P({\mathfrak b})$ denote its polynomial algebra, and suppose that condition (D1),…

Poisson-normalizer extension conjecture. Every integrable irreducible representation of $\wp({\cal B})$ can be extended to a quantization of

Dense basic-set existence conjecture. There exists a nontrivial quantization of

Groenewold–Van Hove conjecture. There is no nontrivial strong quantization of

Let $\mathbf{L_H(d)}$ be the Fourier transform associated with the Lagrangian correspondence $\mathbb L_H(d)$, and let $\mathbf{q\text{-}L_H(d)}$ be its quantization to a functor ……

Let $\mathcal{O}_1$ be the principal orbit in $\mathbb{P}^2(\mathbb{Q})$, and let $\mathcal{Q}(p)$ be the set of quantizations of $p\in\mathcal{O}_1$ in…

Let $X$ be a Calabi–Yau curve and let $ξ$ be a simple vector bundle on $X$. Let $N(ξ)$ be the coarse moduli scheme of the moduli stack of non-splitting complexes $O_X\to V$ such th…

Let $\mathbb{S}^{d-1}$ be the unit sphere, and consider codebooks consisting of points on this sphere. A simplex codebook is a maximally separated codebook; the paper also consider…

Let $U^M=(U_1,\ldots,U_M)$ be a rotationally symmetric codebook, and let $k$-closest encoding denote the proposed encoding scheme that selects the $k$ closest codewords to the inpu…

Let $k\geq 2$, let $(p_1,p_2,\ldots,p_{k-1})$ be a permutation of $\{1/2,1/2^2,\ldots,1/2^{k-1}\}$, and define the probability measure … on $\mathbb{R}$, supported on $\mathbb{N}$.…

Let $f:\mathbb{C}^{m}\to\mathbb{R}$ be a classical Hamiltonian, let $\mathcal{E}_{b}(f(\vec{Z}))$ be its quantization, and define … Let $N_b$ be the number operator and $E_b$ the p…

Let $Z$ be a Poisson algebra, and let $A$ be a quantization of $Z$. Quantization cancellation conjecture. $Z$ is Poisson cancellative if and only if $A$ is cancellative. This propo…

Let a Lie-quasi bialgebroid be a quasi-bialgebroid generalising Lie bialgebroids and quasi-bialgebras, and let a quasi-quantum groupoid be a topological deformation of the standard…

Let a universal quantization of Lie bialgebroids mean a quantization whose formulas are given by expansions in terms of graphs with universal coefficients, and let a quantum groupo…

Let $(E,E^*)$ be a Lie bialgebroid. A quantization is a topological deformation of the standard associative bialgebroid structure on the universal enveloping algebra…

An asymptotically scale-invariant centered MRQ is a family of centered multi-resolution quantizers $\{Q_s\}_{s>0}$ whose asymptotic distribution function is denoted by…

Let $X_1,X_2,X_3\in\operatorname{Mat}(N\times N,\mathbb{C})$ be self-adjoint operators depending on $N$ and satisfying … Assume that there is a constant $c$ such that … for…

Polygonal quantization conjecture. The quantization coefficient for the uniform distribution on the boundary of a regular $m$-sided polygon inscribed in a circle is an increasing f…