Representations of Yangians associated with skew Young diagrams

The Yangian of the Lie algebra $g{l}_N$ 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 $g{l}_N$ by means of the Young symmetrizers. We explicitly construct analogues of these elementary representations for the twisted Yangian, which corresponds to the Lie algebra $s{o}_N$. 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.