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

TL;DR

This paper develops a theory for highest weight representations of twisted Yangians of types B, C, D and classifies their finite-dimensional irreducible representations for certain symmetric pairs.

Contribution

It introduces a new theoretical framework for twisted Yangians of types B, C, D and classifies their finite-dimensional irreducible representations for specific symmetric pairs.

Findings

Established a classification of finite-dimensional irreducible representations.

Developed a theory of highest weight representations for twisted Yangians.

Extended understanding of algebraic structures related to symmetric pairs.

Abstract

We initiate a theory of highest weight representations for twisted Yangians of types B, C, D and we classify the finite-dimensional irreducible representations of twisted Yangians associated to symmetric pairs of types CI, DIII and BCD0.