Document Type
Article
Publication Date
2-16-2021
Publication Title
Algebraic Combinatorics
Volume
4
Issue
1
Pages
163-174
Publisher Name
Centre Mersenne
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.
Recommended Citation
Tingley, Peter. A Quiver Variety Approach to Root Multiplicities. Algebraic Combinatorics, 4, 1: 163-174, 2021. Retrieved from Loyola eCommons, Mathematics and Statistics: Faculty Publications and Other Works, http://dx.doi.org/10.5802/alco.158
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright Statement
© The Journal and the Authors, 2021.
Comments
Author Posting © The Journal and the Authors, 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The article was published in Algebraic Combinatorics, Volume 4, Issue 1, February 2021, https://doi.org/10.5802/alco.158.