Odd reflections in the Yangian associated with \({\frak gl}(m|n)\)

A. I. Molev


The odd reflections is 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 \({\rm Y}({\frak gl}_{m|n})\) 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.

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Wednesday, September 29, 2021