J. Korean Math. Soc. 1997; 34(2): 453-467
Printed June 1, 1997
Copyright © The Korean Mathematical Society.
Jose Maria P. Balmaceda
University of the Philippines
A transitive permutation representation of a group $G$ is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where $H$ is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups $H$ for which $(1_H)^{A_n}, n > 18,$ is multiplicity-free.
Keywords: multiplicity-free permutation representations, alternating groups, permutation characters
MSC numbers: 20B35, 20C15
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