Odd reflections in the Yangian associated with $\mathfrak{g}l(m|n)$

Abstract

The odd reflections are an effective tool in the Lie superalgebra representation theory, as they relate non-conjugate Borel subalgebras. We introduce analogues of the odd reflections for the Yangian $\mathrm{Y}({\mathfrak{g}l}_{m|n})$ and use them to produce a transition rule for the parameters of the highest weight modules corresponding to a change of the parity sequence. This leads to a description of the finite-dimensional irreducible representations of the Yangian associated with an arbitrary parity sequence.

arXiv comment14 pages, minor changes

References in corpus (9)

• Parabolic presentations of the Yangian Y(gl_n)
• Gauss Decomposition of the Yangian Y(gl_{m|n})
• The gl(M|N) Super Yangian and Its Finite Dimensional Representations
• R-matrix presentation for (super)-Yangians Y(g)
• Principal W-algebras for GL(m|n)
• Shuffle algebra realizations of type $A$ super Yangians and quantum affine superalgebras for all Cartan data
• Representations of Super Yangian
• Finite W-superalgebras and truncated super Yangians
• Parabolic presentations of the super Yangian $Y({\mathfrak{gl}}_{M|N})$ associated with arbitrary 01-sequences

Cited by in corpus (6)

• A note on odd reflections of super Yangian and Bethe ansatz
• Representations of the super Yangians of types $A$ and $C$
• Representations of the super-Yangian of type $B(n,m)$
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• Representations of the super-Yangian of type $D(n,m)$
• Twisted super Yangians of type AIII and their representations