Algebra & Number Theory

The 2-block splitting in symmetric groups

Christine Bessenrodt

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Abstract

In 1956, Brauer showed that there is a partitioning of the p-regular conjugacy classes of a group according to the p-blocks of its irreducible characters with close connections to the block theoretical invariants. But an explicit block splitting of regular classes has not been given so far for any family of finite groups. Here, this is now done for the 2-regular classes of the symmetric groups. To prove the result, a detour along the double covers of the symmetric groups is taken, and results on their 2-blocks and the 2-powers in the spin character values are exploited. Surprisingly, it also turns out that for the symmetric groups the 2-block splitting is unique.

Article information

Source
Algebra Number Theory, Volume 1, Number 2 (2007), 223-238.

Dates
Received: 3 May 2007
Revised: 2 July 2007
Accepted: 8 August 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513797128

Digital Object Identifier
doi:10.2140/ant.2007.1.223

Mathematical Reviews number (MathSciNet)
MR2361941

Zentralblatt MATH identifier
1160.20010

Subjects
Primary: 20C30: Representations of finite symmetric groups
Secondary: 20C15: Ordinary representations and characters 20C20: Modular representations and characters

Keywords
symmetric groups $p$-regular conjugacy classes Cartan matrix irreducible characters Brauer characters $p$-blocks spin characters

Citation

Bessenrodt, Christine. The 2-block splitting in symmetric groups. Algebra Number Theory 1 (2007), no. 2, 223--238. doi:10.2140/ant.2007.1.223. https://projecteuclid.org/euclid.ant/1513797128


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References

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