A note on odd reflections of super Yangian and Bethe ansatz

Abstract

In a recent paper arXiv:2109.09462, Molev introduced analogues of the odd reflections for the super Yangian $\mathrm{Y}({\mathfrak{gl}}_{m|n})$ and obtained a transition rule for the change of highest weights when the parity sequence is altered. In this note, we reproduce the results from a different point of view and discuss their relations with the fermionic reproduction procedure of the XXX-type Bethe ansatz equations introduced in arXiv:1811.11225. We give an algorithm that how the $q$-characters change under the odd reflections. We also take the chance to compute explicitly the $q$-characters of skew representations of $\mathrm{Y}({\mathfrak{gl}}_{m|n})$ for arbitrary parity sequences.

21 pages. This note is a continuation of arXiv:2007.15573 and arXiv:2103.08758. V2: fixed typos and grammar mistakes, added remarks and references

References in corpus (5)

• Gauss Decomposition of the Yangian Y(gl_{m|n})
• Representations of the super Yangians of types $A$ and $C$
• Bethe ansatz equations for orthosymplectic Lie superalgebras and self-dual superspaces
• Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
• Odd reflections in the Yangian associated with $\mathfrak{g}l(m|n)$

Cited by in corpus (4)

• Completeness of Bethe ansatz for Gaudin models associated with gl(1|1)
• Representations of the super-Yangian of type $B(n,m)$
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• Twisted super Yangians of type AIII and their representations