Parabolic presentations of the super Yangian $Y(\mathfrak{gl}_{M|N})$ associated with arbitrary 01-sequences

TL;DR

This paper introduces a new algebraic presentation of the super Yangian associated with the general linear Lie superalgebra, based on arbitrary compositions and sequences, enhancing understanding of its structure.

Contribution

It provides a novel parabolic presentation of the super Yangian $Y(rak{gl}_{M|N})$ for arbitrary compositions and sequences, broadening the algebra's structural insights.

Findings

New algebraic presentation of super Yangian $Y(rak{gl}_{M|N})$

Applicable to arbitrary compositions and sequences

Facilitates further structural and representation theory studies

Abstract

For any fixed composition $\mu$ of $M+N$ and any fixed $0^M1^N$-sequence $\mathfrak{s}$, we obtain a new presentation of the super Yangian $Y_{M|N}$ associated to the general linear Lie superalgebra $\mathfrak{gl}_{M|N}$.