Parabolic Presentations of the Super Yangian $${Y(\mathfrak{gl}_{M|N})}$$ Y ( gl M | N ) Associated with Arbitrary 01-Sequences

PARABOLIC PRESENTATIONS OF THE YANGIAN Y (gln)

We introduce some new presentations for the Yangian associated to the Lie algebra gln. These presentations are parametrized by tuples of positive integers summing to n. At one extreme, for the tuple (n), the presentation is the usual RTT presentation of Yn. At the other extreme, for the tuple (1 ), the presentation is closely related to Drinfeld’s presentation. In general, the presentations are...

Gauss Decomposition of the Yangian Y (gl M|n )

We describe a Gauss decomposition for the Yangian Y (glm|n) of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie superalgebra Y (A(m− 1, n− 1)) (with m 6= n) defined and studied in papers by Stukopin, and suggests natural definitions for the Yangians Y (sln|n) and Y (A(n, n)). We also show that the coefficients of the quantum ...

A Recent Look at the Quantum Berezinian in the Yangian Y (gl M|n )

Brundan and Kleshchev recently introduced a new family of presentations of the Yangian Y (gln) associated to the general linear Lie algebra gln, and thus provided a fresh approach to its study. In this article, we would like to show how some of their ideas can be fruitfully extended to consider the Yangian Y (glm|n) associated to the Lie superalgebra glm|n. In particular, we give a new proof of...

The gl(M|N) Super Yangian and Its Finite Dimensional Representations

Polynomial super-gl(n) algebras

We introduce a class of finite dimensional nonlinear superalgebras L = L0 + L1 providing gradings of L0 = gl(n) ' sl(n) + gl(1). Odd generators close by anticommutation on polynomials (of degree > 1) in the gl(n) generators. Specifically, we investigate ‘type I’ super-gl(n) algebras, having odd generators transforming in a single irreducible representation of gl(n) together with its contragredi...