Speaker
Description
We present some results on the double Yangian associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$. We establish the Poincaré-Birkhoff-Witt Theorem for the double Yangian. Then, we construct the dual counterpart of the quantum contraction for the dual Yangian and we show that its coefficients are central elements. As an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and we find their presentations by generators and relations. Finally we generalize the notion of quantum Berezinian to the double Yangian associated with $\mathfrak{gl}_{m|n}$ and we show that its coefficients form a family of algebraically independent topological generators of the center of $DY(\mathfrak{gl}_{m|n})$.
