English

A quiver variety approach to root multiplicities

Representation Theory 2021-02-24 v2 Quantum Algebra

Abstract

We present combinatorial upper bounds on dimensions of certain imaginary root spaces for symmetric Kac-Moody algebras. These come from the realization of the corresponding infinity-crystal using quiver varieties. The framework is general, but we only work out specifics in rank two. In that case we give explicit bounds. These turn out to be quite accurate, and in many cases exact, even for some fairly large roots.

Keywords

Cite

@article{arxiv.1910.04637,
  title  = {A quiver variety approach to root multiplicities},
  author = {Peter Tingley},
  journal= {arXiv preprint arXiv:1910.04637},
  year   = {2021}
}

Comments

Includes an appendix coauthored with Colin Williams