Multiplicity-free representations of symmetric groups
Abstract
Building on work of Saxl, we classify the multiplicity-free permutation characters of all symmetric groups of degree 66 or more. A corollary is a complete list of the irreducible characters of symmetric groups (again of degree 66 or more) which may appear in a multiplicity-free permutation representation. The multiplicity-free characters in a related family of monomial characters are also classified. We end by investigating a consequence of these results for Specht filtrations of permutation modules defined over fields of prime characteristic. Remark: parallel work of Godsil and Meagher (arXiv:math/0612567) gives an independent classification of the multiplicity-free permutation characters of symmetric groups of all degrees.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2009
- DOI:
- 10.48550/arXiv.0903.2864
- arXiv:
- arXiv:0903.2864
- Bibcode:
- 2009arXiv0903.2864W
- Keywords:
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- Mathematics - Representation Theory;
- 20C30;
- 20C20
- E-Print:
- 23 pages, 4 figures