Date of Award
2021
Document Type
Honors Thesis (Open Access)
Department
Colby College. Mathematics and Statistics Dept.
Advisor(s)
Tamar Friedmann
Second Advisor
Fernando Gouvêa
Abstract
Given a compact exceptional group $G$ and $m,s\in\mathbb{N}$, let $N(G,m)$ be the number of conjugacy classes of elements of order $m$ in $G$, and $N(G,m,s)$ the number of such classes whose elements have $s$ distinct eigenvalues. In string theory, the problem of enumerating certain classes of vacua in the string landscape can be rephrased in terms of the study of these quantities. We develop unified combinatorial algorithms based on Burnside's Lemma that can be used to compute both quantities for each of the five compact exceptional groups. Thus, we provide a combinatorial, alternative method to that of Djoković and extend previous results obtained by Friedmann-Stanley for the compact classical groups.
Keywords
Conjugacy classes, finite order, Lie groups, Burnside's Lemma, Möbius inversion
Recommended Citation
He, Qidong, "Counting Conjugacy Classes of Elements of Finite Order in Compact Exceptional Groups" (2021). Honors Theses. Paper 1314.https://digitalcommons.colby.edu/honorstheses/1314