Representations of the alternating group which are irreducible over subgroups, II

Alexander Kleshchev; Peter Sin; Pham Huu Tiep

doi:10.1353/ajm.2016.0041

Representations of the alternating group which are irreducible over subgroups, II

Alexander Kleshchev
, Peter Sin
, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove that non-trivial representations of the alternating group A_n are reducible over a primitive proper subgroup which is isomorphic to some alternating group A_m. A similar result is established for finite simple classical groups embedded in A_n via their standard rank 3 permutation representations.

Original language	English (US)
Pages (from-to)	1383-1423
Number of pages	41
Journal	American Journal of Mathematics
Volume	138
Issue number	5
DOIs	https://doi.org/10.1353/ajm.2016.0041
State	Published - Oct 2016

ASJC Scopus subject areas

General Mathematics

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title = "Representations of the alternating group which are irreducible over subgroups, II",

abstract = "We prove that non-trivial representations of the alternating group An are reducible over a primitive proper subgroup which is isomorphic to some alternating group Am. A similar result is established for finite simple classical groups embedded in An via their standard rank 3 permutation representations.",

author = "Alexander Kleshchev and Peter Sin and Tiep, \{Pham Huu\}",

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year = "2016",

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doi = "10.1353/ajm.2016.0041",

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AU - Kleshchev, Alexander

AU - Sin, Peter

AU - Tiep, Pham Huu

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N2 - We prove that non-trivial representations of the alternating group An are reducible over a primitive proper subgroup which is isomorphic to some alternating group Am. A similar result is established for finite simple classical groups embedded in An via their standard rank 3 permutation representations.

AB - We prove that non-trivial representations of the alternating group An are reducible over a primitive proper subgroup which is isomorphic to some alternating group Am. A similar result is established for finite simple classical groups embedded in An via their standard rank 3 permutation representations.

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DO - 10.1353/ajm.2016.0041

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EP - 1423

JO - American Journal of Mathematics

JF - American Journal of Mathematics

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Representations of the alternating group which are irreducible over subgroups, II

Abstract

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