Details
| Original language | English |
|---|---|
| Pages (from-to) | 223-238 |
| Number of pages | 16 |
| Journal | Algebra and Number Theory |
| Volume | 1 |
| Issue number | 2 |
| Publication status | Published - 1 May 2007 |
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.
Keywords
- Brauer characters, Cartan matrix, Irreducible characters, P-blocks, P-regular conjugacy classes, Spin characters, Symmetric groups
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Algebra and Number Theory, Vol. 1, No. 2, 01.05.2007, p. 223-238.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The 2-block splitting in symmetric groups
AU - Bessenrodt, Christine
PY - 2007/5/1
Y1 - 2007/5/1
N2 - 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.
AB - 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.
KW - Brauer characters
KW - Cartan matrix
KW - Irreducible characters
KW - P-blocks
KW - P-regular conjugacy classes
KW - Spin characters
KW - Symmetric groups
UR - http://www.scopus.com/inward/record.url?scp=77954007131&partnerID=8YFLogxK
U2 - 10.2140/ant.2007.1.223
DO - 10.2140/ant.2007.1.223
M3 - Article
AN - SCOPUS:77954007131
VL - 1
SP - 223
EP - 238
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 2
ER -