Representations of twisted Yangians of types B, C, D: II

TL;DR

This paper advances the understanding of finite-dimensional irreducible representations of twisted Yangians of types B, C, D, providing classification results for specific symmetric pairs and establishing necessary conditions on highest weights.

Contribution

It classifies finite-dimensional irreducible representations of twisted Yangians for certain symmetric pairs and establishes relations for highest weights across types B, C, D.

Findings

Necessary relations for highest weights of modules.

Classification of representations for specific symmetric pairs.

Extension of previous results to types BI, CII, DI.

Abstract

We continue the study of finite-dimensional irreducible representations of twisted Yangians associated to symmetric pairs of types B, C and D, with focus on those of types BI, CII and DI. After establishing that, for all twisted Yangians of these types, the highest weight of such a module necessarily satisfies a certain set of relations, we classify the finite-dimensional irreducible representations of twisted Yangians for the pairs $(\mathfrak{so}_N,\mathfrak{so}_{N-2} \oplus \mathfrak{so}_2)$ and $(\mathfrak{so}_{2n+1},\mathfrak{so}_{2n})$.