15 problems

Let $I_0$ index the fundamental representations, let $R^{{\operatorname{nor}}}_{ij}(x,y)$ be the normalized $R$-matrix for $i,j\in I_0$, and let $\gamma$ be the parameter defined i…

Let $I_0$ index the fundamental representations, let $i_1,\ldots,i_l\in I_0$, and let $a_1,\ldots,a_l\in\bar k^\times$, where $\bar k=\bigcup_{n>0}\mathbb C((q^{1/n}))$. Write…

Braided tangent-field conjecture. Equations (4) hold if we replace $U_i$ by $U_i^q$ and $f_{\beta,i}$ by $f_{\beta,i}(q)$.

Let $R$ be a unitary involutive $R$-matrix. An invertible matrix $\alpha$ is assumed to satisfy the relation referred to as Eq. (Ralphadef-graphical), and $\theta$ denotes the part…

Let $m,p\in 2\mathbb{Z}_{\geq 1}+1$, let $k<n$, and let $\mathfrak{g}=C_n^{(1)}$. Write $d_{k^m,k^p}(z)$ for the denominator polynomial of the corresponding normalized $R$-matrix,…

Let $X$ be the complete intersection of two quadric hypersurfaces in $\mathbb{CP}^5$, and let $\Sigma_2$ be a genus $2$ surface. Suppose an R-matrix relates the two splittings of t…

Let $\mathsf{F}$ be the Fock space, let $\mathsf{RR}^{H}_{\mathsf{F},\mathsf{F}\otimes\mathsf{F}}$ denote the four-point operator in cohomological DT theory, and let…

Hopf algebra isomorphism conjecture. The map $\Upsilon$ induces a Hopf algebra isomorphism

R-matrix correspondence conjecture. The endomorphism

Let $\mathfrak{O}(V^{(i)}_k,V^{(j)}_l)$ be the divisor of the normalized $R$-matrix denominator, and let $\dim_{q^{-1}}\mathop{\mathrm{ext}}^1_{\widetilde{\Pi}}$ denote the graded…

Let $I$ index the simple roots, let $d_i$ be the symmetrizing integers, let $r$ and $h^\vee$ be the parameters used in the paper, and let $\widetilde{c}_{ij}(u)$ be the coefficient…

Okounkov's shift-operator R-matrix conjecture. In the stable basis, the operator $S_\mathsf{w}$ is conjugate to the R-matrix for

Let $p$ be the momentum of a massless mode and define the non-relativistic rapidity … For relativistic massless scattering, let $\theta$ denote the rapidity difference, and let rig…

Let $U_{q,p}([...??]$ be the elliptic quantum algebra with half currents assembled into the $L$-operator $[...??]$. For two auxiliary tensor components, write $[...??]$ and let…

Let $m$ and $n$ be relatively prime positive integers with $m<n$. Let $\mathfrak{p}_{m,n}\subseteq\mathfrak{sl}_n$ be the maximal parabolic subalgebra obtained by deleting the $m$-…