Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MULTIPLICITY-FREE ACTIONS OF THE ALTERNATING GROUPS

  • Balmaceda, Jose Maria P. (Department of Mathematics University of the Philippines Diliman)
  • Published : 1997.05.01
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Abstract

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 $(1_H)^An, n > 18$, is multiplicity-free.

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References

  1. Cambridge Studies in Adv. Math. 10 Finite Group Theory M. Aschbacher
  2. Multiplicity-free permutation representations of the alternating groups, Ph. D. Thesis J.M. P. Balmaceda
  3. On some permutation characters of the alternating groups J. M. P. Balmaceda
  4. Finite Groups III, Grundlehren der Math. Wiss. v.243 N. Blackburn;B. Huppert
  5. Comm. in Alg. v.24 no.7 The multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups T. Breuer;K. Lux
  6. Character Theory of Finite Groups I.M. Isaacs
  7. The Representation Theory of the Symmetric Group, Encyclopedia of Math. and its Applic. v.16 G. James;A. Karber
  8. Bull. Austral. Math. Soc. v.35 Distance-transitive graphs with symmetric or alternating automorphism group M. W. Liebeck;C. E. Praeger;J. Saxl
  9. Bull. London Math. Soc. v.12 On the orders of primitive permutation groups C. E. Praeger;J. Saxl
  10. London Math. Soc. Lecture Notes v.49 On multiplicity-free permutation representations, in Finite Geometries and Designs J. Saxl