Symmetric group blocks of small defect

2003/11/23 by Gordon James, James, Gordon, Andrew Mathas +1
Mathematics · #20C30 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:20C30

paper · pdf · doi:10.48550/arxiv.math/0311408

42 pages

arxiv created 2003/11/23 · arxiv updated 2009/12/01

Abstract

This paper is an attempt to compute the decomposition numbers of the blocks of the symmetric group which have "small defect"; that is, blocks of weight smaller than the characteristic. We present various methods for computing such decomposition numbers and use these as support for a conjecture which relates decomposition numbers in different characteristics. Finally, we apply our techniques to blocks of weight three.

Related

• Defect 2 spin blocks of symmetric groups and canonical basis coefficients
• On 2-blocks with minimal nonabelian defect groups II
• Blocks of small defect
• Refinements of the orthogonality relations for blocks
• Conjectures of Alperin and Broue for 2-blocks with elementary abelian defect groups of order 8