Representations of Yangians associated with skew Young diagrams
Abstract
Description
The 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 pages
12 pages