7 problems

Master pentagon identity. The generating functions satisfy

Let $I(s_1/s_0,\ldots,s_N/s_0)$ be the integral operator introduced in the cited works, and let Macdonald's difference operator act on the relevant functions. Shiraishi's commutati…

Let $cmathcal{A}(N)$ be the algebra generated by the modes $X^{(i)}_n$ acting on the Fock module $cmathcal{F}_{\vec{u}}$, and let $Ket{X_{\vec{\lambda}}}$ and…

Let $cmathcal{U}$ be the DingIoharaMiki algebra, let $cmathcal{A}(N)$ be its algebra generated by the currents $X^{(i)}_n$, and let $Ket{X_{\vec{\lambda}}}$ denote the integral-for…

Let $cmathcal{U}$ be the DingIoharaMiki algebra, let $cmathcal{A}(N)$ be the algebra generated by the currents $X^{(i)}_n$, and let $Ket{X_{\vec{\lambda}}}$ be the PBW-type vectors…

Uniqueness-normalized universal R-matrix conjecture. With this normalization, the R-matrix obtained in the article satisfies both defining equations above, because there is only on…

Let $X^{(i)}_n$ ($i=1,\ldots,N$, $n\in\mathbb{Z}$) be the generating operators acting on the highest-weight module $\mathcal{F}_{\vec{u}}$ with highest-weight vector…