Involutive automorphism of symmetric groups. (English) Zbl 1392.20002
Summary: Let \((\mathfrak{S}_n,S)\) be a Coxeter system of the symmetric group, we show that the set of automorphisms of \(\mathfrak{S}_n\) which are involutions and leave \(S\) stable is a finite group of order less than 3.
MSC:
| 20B30 | Symmetric groups |
| 20B35 | Subgroups of symmetric groups |
| 05E10 | Combinatorial aspects of representation theory |
References:
| [1] | Björner, A.; Brenti, F., Combinatorics of Coxeter groups, 231, (2005), Springer-Verlage, New York · Zbl 1110.05001 |
| [2] | Hu, J.; Zhang, J., On involutions in symmetric groups and a conjecture of Lusztig, Adv. Math., 287, 1-30, (2016) · Zbl 1338.20004 |
| [3] | Lusztig, G., Asymptotic Hecke Algebras and Involutions · Zbl 1301.20005 |
| [4] | Lusztig, G., An involution base left ideal in the Hecke algebra, Represent. Theory, 19, 172-186, (2016) · Zbl 1378.20004 |
| [5] | Rotman, J.-J., An Introduction to the Theory of Groups, 148, (1994), Springer-Verlage, New York · Zbl 0810.20001 |
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