13 problems

The XXZ model is considered through ground-state averages of local operators in finite, possibly inhomogeneous, chains, with the reduced quantum Knizhnik–Zamolodchikov (rqKZ) equat…

The level-zero qKZ equation has hypergeometric solutions constructed by the method introduced for the $\mu=0$ case, and these solutions can satisfy linear relations. Completeness c…

Conjecture. The constructions give the same result for any irreducible finite-dimensional representation of $U_q(\widehat{\mathfrak{gl}}_N)$.

The rational quantized Knizhnik–Zamolodchikov difference equations have hypergeometric solutions, and the corresponding dynamical differential equations are defined for the same se…

The q-Knizhnik–Zamolodchikov (qKZ) equations are q-difference equations whose connection matrices describe their q-monodromy. An elliptic quantum group is the appropriate elliptic…

Let $\Psi^{(L)}(\tau)$ be the homogeneous open boundary qKZ solution, and let $\pi_{\max}$ connect points $2i-1$ to $2i$, with the last point unmatched when $L$ is odd. Let…

Let $\Psi^{(L)}(\tau)$ be the homogeneous open boundary qKZ solution, let $L$ be its size, and let $N_8(L+1;\tau)$ and $A_V(L+1;\tau)$ denote the generating polynomials for the cor…

Let $\Psi^{(L)}(\tau)$ be the homogeneous open boundary quantum Knizhnik–Zamolodchikov solution, with components indexed by link patterns, and let the admissible endpoints of link…

Let $q$ be a generic parameter, and consider the higher-spin loop model with fusion level $\ell$. The unfused model has a level-$1$ (“free boson”) quantum KnizhnikZamolodchikov (…

The polynomials arise from orbital varieties for the classical series $B_r$, $C_r$, and $D_r$, and their homogeneous limits are obtained by setting the spectral parameters equal. S…

Massless-regime equality conjecture. The equality

Let $V_1,V_2$ be finite-dimensional representations, let $\a0\lambda\in\mathfrak{h}$ be a dynamical parameter, and consider the Frenkel–Reshetikhin $q$KZ equation … Here…

Let $\psi_{\alpha}(x_1,\ldots,x_L)$ be the components of the polynomial solution of the qKZ equation of type A, evaluated in the limit $x_i\rightarrow 0$ for $i=1,\ldots,L$, and le…