8 problems

Let $M$ be a finite-dimensional irreducible $\mathrm{Y}(\mathfrak{gl}_{m|n})$-module of highest $\ell$-weight $\boldsymbol\zeta=(\zeta_i(u))_{i\in\bar I}^s$. Let…

A sufficient condition for the existence of irreducible finite-dimensional representations has been given in earlier work. It gives an explicit construction as a tensor product of…

Let $D(2,1;\lambda)$ be the exceptional Lie superalgebra with Dynkin diagrams $G(D_{\lambda})$ and $G(D_{\lambda}^{\circ})$ related by the odd reflection $s_{\alpha_2}$, and let…

Let $\mathrm{Y}(\mathfrak{gl}_{m|n})$ be the super-Yangian associated with the finite-dimensional complex Lie superalgebra $\mathfrak{gl}_{m|n}$, and let the quantum Berezinian den…

Let ${\mathscr{B}_{\bm s,\bm \varepsilon}}$ be the twisted super Yangian of type AIII, let $V(\bm\mu(u))$ be an irreducible ${\mathscr{B}_{\bm s,\bm \varepsilon}}$-module, and let…

Let $\mathrm{Y}(\mathfrak{gl}_{m|n})$ be the super Yangian. A finite-dimensional irreducible module is tame and thin according to the weight-space conditions for…

Let $\mathrm{Y}(\mathfrak{gl}_{m|n})$ be the super Yangian, and call a finite-dimensional irreducible module tame or thin according to the weight-space conditions used for these mo…

Let $\mathrm{Y}(\mathfrak{gl}_{m|n})$ be the super Yangian, and let its Bethe subalgebra be the commutative subalgebra generated by the coefficients of the quantum Berezinian. A di…