Details
| Original language | English |
|---|---|
| Pages (from-to) | 1774-1788 |
| Number of pages | 15 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 119 |
| Issue number | 8 |
| Early online date | 12 Jun 2012 |
| Publication status | Published - Nov 2012 |
Abstract
In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on restricted sets of conjugacy classes, like beautiful combinatorial determinant formulae for submatrices of the character table and Cartan matrices with respect to basic sets; we observe that similar phenomena occur for the transition matrices between power sum symmetric functions to bounded partitions and the k-Schur functions defined by Lapointe and Morse. Arithmetic properties of the numbers occurring in this context are studied via generating functions.
Keywords
- Basic sets, Cartan matrices, Character tables, Determinants, Generating functions, K-Schur functions, Symmetric groups
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Computer Science(all)
- Computational Theory and Mathematics
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In: Journal of Combinatorial Theory. Series A, Vol. 119, No. 8, 11.2012, p. 1774-1788.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Submatrices of character tables and basic sets
AU - Bessenrodt, Christine
AU - Olsson, Jørn B.
N1 - Funding Information: The authors would like to thank the Danish Research Council (FNU) for the support of their collaboration. We also express our thanks to Anne Schilling for sharing her data on k-Schur functions at the meeting on Algebraic Combinatorixx at the Banff International Research Station (BIRS), 2011, and for pointing out a result by Lapointe and Morse. Thanks go also to the referees for their helpful suggestions and comments.
PY - 2012/11
Y1 - 2012/11
N2 - In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on restricted sets of conjugacy classes, like beautiful combinatorial determinant formulae for submatrices of the character table and Cartan matrices with respect to basic sets; we observe that similar phenomena occur for the transition matrices between power sum symmetric functions to bounded partitions and the k-Schur functions defined by Lapointe and Morse. Arithmetic properties of the numbers occurring in this context are studied via generating functions.
AB - In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on restricted sets of conjugacy classes, like beautiful combinatorial determinant formulae for submatrices of the character table and Cartan matrices with respect to basic sets; we observe that similar phenomena occur for the transition matrices between power sum symmetric functions to bounded partitions and the k-Schur functions defined by Lapointe and Morse. Arithmetic properties of the numbers occurring in this context are studied via generating functions.
KW - Basic sets
KW - Cartan matrices
KW - Character tables
KW - Determinants
KW - Generating functions
KW - K-Schur functions
KW - Symmetric groups
UR - http://www.scopus.com/inward/record.url?scp=84861963499&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2012.06.001
DO - 10.1016/j.jcta.2012.06.001
M3 - Article
AN - SCOPUS:84861963499
VL - 119
SP - 1774
EP - 1788
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
SN - 0097-3165
IS - 8
ER -