کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4653592 | 1632783 | 2014 | 11 صفحه PDF | دانلود رایگان |
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.
Journal: European Journal of Combinatorics - Volume 36, February 2014, Pages 86–96