English

Rational representations of the Yangian Y(gl_n)

Representation Theory 2013-09-11 v1 Quantum Algebra

Abstract

We construct a series of rational representations of Y(gl_n) and intertwining operators between them. We find explicit expressions for the images of highest-weight vectors under the intertwining operators. Finally, we state a conjecture that all irreducible finite-dimensional rational Y(gl_n)-modules arise as images of the constructed intertwining operators.

Keywords

Cite

@article{arxiv.1309.1822,
  title  = {Rational representations of the Yangian Y(gl_n)},
  author = {Alexander Shapiro},
  journal= {arXiv preprint arXiv:1309.1822},
  year   = {2013}
}

Comments

Formula for the image of the highest weight vector in the skew-symmetric case is corrected from the print version. This text, being a continuation of the series of papers [KN1], [KN2], [KN3], [KN4] closely (sometimes literally, when appropriate) follows the exposition of the mentioned works arXiv:math/0606265, arXiv:math/0703651, arXiv:math/0606272, arXiv:0801.0519