Counting conjugacy classes of elements of finite order in Lie groups
Name
Stanely_Counting conjugacy.pdf
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148.45 KB
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Author(s)
Friedmann, Tamar
Stanley, Richard P
Date Issued
August 2013
Journal
European Journal of Combinatorics
Publisher
Elsevier
Citation
Friedmann, Tamar and Stanley, Richard P. “Counting Conjugacy Classes of Elements of Finite Order in Lie Groups.” European Journal of Combinatorics 36 (February 2014): 86–96 © 2013 Published by Elsevier Ltd
Version
Author's final manuscript
Abstract
Using combinatorial techniques, we answer two questions about simple classical Lie groups. Define N(G,m)N(G,m) to be the number of conjugacy classes of elements of finite order mm in a Lie group GG, and N(G,m,s)N(G,m,s) to be the number of such classes whose elements have ss distinct eigenvalues or conjugate pairs of eigenvalues. What is N(G,m)N(G,m) for GG a unitary, orthogonal, or symplectic group? What is N(G,m,s)N(G,m,s) for these groups? For some cases, the first question was answered a few decades ago via group-theoretic techniques. It appears that the second question has not been asked before; here it is inspired by questions related to enumeration of vacua in string theory. Our combinatorial methods allow us to answer both questions.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.ejc.2013.06.046
