Representations of Yangians associated with skew Young diagrams

Details Representations of Yangians associated with skew Young diagrams Representations of Yangians associated with skew Young diagrams

2002-09-11

arxiv.org/abs/math/0209129v1

Proceedings of the ICM, Beijing 2002, vol. 2, 643--654

Mathematics

Representation Theory

12 pages

Scientific paper

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.

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