4 problems

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…

Higher-Hamiltonian eigenvalue conjecture.

Let $\vec{\lambda}$ and $\vec{\mu}$ be $N$-tuples of Young diagrams, and let $c^{(\pm)}_{\vec{\lambda},\vec{\mu}}(q,t\mid u_1,\ldots,u_N)$ be the coefficients in the action … For a…

Conjectural action of $X^{(1)}_{\pm1}$.