Document Type
Article
Publication Date
2-2014
Abstract
Using combinatorial techniques, we answer two questions about simple classical Lie groups. Define N(G,m) to be the number of conjugacy classes of elements of finite order m in a Lie group G, and N(G,m,s) to be the number of such classes whose elements have s distinct eigenvalues or conjugate pairs of eigenvalues.What is N(G,m) for G a unitary, orthogonal, or symplectic group?What is 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.
Volume
36
First Page
86
Last Page
96
DOI
doi.org/10.1016/j.ejc.2013.06.046
Rights
© the authors
Recommended Citation
Friedmann, Tamar and Stanley, Richard P., "Counting Conjugacy Classes of Elements of Finite Order in Lie Groups" (2014). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/72
Comments
Peer reviewed accepted manuscript.