Infinite-rank Euclidean Lattices and Loop Groups
Representation Theory
2023-01-04 v2
Abstract
In this paper, we associate a family of infinite-rank pro-Euclidean lattices to elements of a formal loop group and a highest weight representation of the underlying affine Kac--Moody algebra. In the case that the element has a polynomial representative, we can prove our lattices are theta-finite in the sense of Bost, allowing us to attach to each of our lattices a well-defined theta-like function.
Cite
@article{arxiv.2203.08976,
title = {Infinite-rank Euclidean Lattices and Loop Groups},
author = {Mathieu Dutour and Manish M. Patnaik},
journal= {arXiv preprint arXiv:2203.08976},
year = {2023}
}
Comments
The title of the previous version was "Infinite rank Hermitian Lattices and Loop Groups". Typos corrected. Convergence lemma added at the end for clarity