10 problems

Let $\mathcal G$ be a simple complex Lie group equipped with a factorizable Lie bialgebra structure, and let $T=(\Gamma_1,\Gamma_2,\gamma)$ be a Belavin–Drinfeld triple for its tan…

A complex semisimple Lie group carries a Poisson–Lie structure associated with a solution of the classical Yang–Baxter equation, parametrized by a Belavin–Drinfeld triple and conti…

The paper compares the trivial and Poisson structures for $SU(2)$, where the symplectic leaves are spheres and the transformation to Darboux coordinates makes the path integrals ha…

Let $V_2$ be the two-dimensional complex Cartan subalgebra for the Lie algebra of type $G_2$, and let $V_2^{\rm reg}$ be the complement of the six root-kernel lines. Let $W_{G_2}$…

Conjecture on the relation between $\Psi$ and $J'$. The quantization $\Psi$ of the PL dynamical $r$-matrix $r_0-r'$ is related to the pseudotwist $J'$ by

Let $V$ be the codimension-$4$ cluster subvariety of the Fock–Goncharov moduli space associated with the punctured disk with four marked boundary points, and let ${\mathcal C}$ be…

Generalized cluster structure conjecture. Any such solution gives rise to a compatible cluster structure on the Lie group.

Let $\mathcal G$ be a simple complex Lie group equipped with a factorizable Poisson–Lie structure arising from a classical $r$-matrix, that is, a solution of the classical Yang–Bax…

Belavin–Drinfeld cluster-structure conjecture. For any Belavin–Drinfeld triple $T=(\Gamma_1,\Gamma_2,\gamma)$ there exists a cluster structure $({\mathcal C}_T,\varphi_T)$ on…

The trigonometric real form called the $\mathrm{III}_{\mathrm{b}}$ system is obtained from gauged WZW theory. Gorsky–Nekrasov conjecture. It should be possible to derive the same s…