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

### A. I. Molev

#### Abstract

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