Year: 2024
Type: preprint
Abstract: Let $G$ be a group and $α: G \times G \to G$ denote the commutator map. In the case of finite groups, Frobenius gave the formula to compute the cardinalities of the fibres $α^{-1}(g)$ in terms of the character values $χ(g)$ for irreducible characters $χ$ of $G$. We generalise this formula to compact Lie groups. Further, we connect this generalised formula to the commutator probability of the concerned groups.
Source: arXiv (Cornell University)
Authors: Garge, Shripad, Sharma, Uday Bhaskar
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403577964