English

Quantum loop algebras and l-root operators

Quantum Algebra 2014-10-01 v2

Abstract

Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data (g,q,P), we define an algebra A whose raising/lowering operators are constructed to act with definite l-weight (unlike those of Uq(Lg) itself). It is shown that there is a homomorphism Uq(Lg) -> A such that every representation V in C_P is the pull-back of a representation of A.

Keywords

Cite

@article{arxiv.1206.6657,
  title  = {Quantum loop algebras and l-root operators},
  author = {C. A. S. Young},
  journal= {arXiv preprint arXiv:1206.6657},
  year   = {2014}
}

Comments

28 pages, latex; v2: Version to appear in Transformation Groups

R2 v1 2026-06-21T21:27:21.896Z