2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64914The Yangian of the Lie algebra $gl_N$ has a distinguished family of irreducible finite-dimensional representations, called elementary representations. They are parametrized by pairs, consisting of a skew Young diagram and a complex number. Each of these representations has an explicit realization, it extends the classical realization of the irreducible polynomial representations of $gl_N$ by means of the Young symmetrizers. We explicitly construct analogues of these elementary representations for the twisted Yangian, which corresponds to the Lie algebra $so_N$. Our construction provides solutions to several open problems in the classical representation theory. In particular, we obtain analogues of the Young symmetrizers for the Brauer centralizer algebra.12 pagesRepresentation TheoryCombinatoricsQuantum Algebra17B35; 17B37; 20C30; 22E46text