Positive level, negative level and level zero
Representation Theory
2019-11-26 v2 Algebraic Geometry
Combinatorics
Abstract
This is a survey on the combinatorics and geometry of integrable representations of quantum affine Lie algebras with a particular focus on level 0. Pictures and examples are included to illustrate the affine Weyl group orbits, crystal graphs and Macdonald polynomials that provide detailed understanding of the structure of the extremal weight modules and their characters. The final section surveys the alcove walk method of working with the positive level, negative level and level zero affine flag varieties and describes the corresponding actions of the affine Hecke algebra.
Cite
@article{arxiv.1907.11796,
title = {Positive level, negative level and level zero},
author = {Finn McGlade and Arun Ram and Yaping Yang},
journal= {arXiv preprint arXiv:1907.11796},
year = {2019}
}