Double Yangian and reflection algebras of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$

Abstract

We study the double Yangian associated with the Lie superalgebra ${\mathfrak{gl}}_{m|n}$. Our main focus is on establishing the Poincaré-Birkhoff-Witt Theorem for the double Yangian and constructing its central elements in the form of coefficients of the quantum contraction. Next, as an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and find their presentations by generators and relations.

19 pages, comments are welcome

References in corpus (3)

• Gauss Decomposition of the Yangian Y(gl_{m|n})
• Jacobi-Trudi identity and Drinfeld functor for super Yangian
• The formal shift operator on the Yangian double

Cited by in corpus (2)

• A note on the quantum Berezinian for the double Yangian of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$
• Twisted super Yangians of type AIII and their representations