Details
| Original language | English |
|---|---|
| Pages (from-to) | 1109-1131 |
| Number of pages | 23 |
| Journal | Algebras and representation theory |
| Volume | 20 |
| Issue number | 5 |
| Publication status | Published - 1 Oct 2017 |
| Externally published | Yes |
Abstract
For a block B of a finite group G there are well-known orthogonality relations for the generalized decomposition numbers. We refine these relations by expressing the generalized decomposition numbers with respect to an integral basis of a certain cyclotomic field. After that, we use the refinements in order to give upper bounds for the number of irreducible characters (of height 0) in B. In this way we generalize results from [Héthelyi-Külshammer-Sambale, 2014]. These ideas are applied to blocks with abelian defect groups of rank 2. Finally, we address a recent conjecture by Navarro.
Keywords
- Abelian defect groups, k(B), Navarro Conjecture, Orthogonality relations
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Algebras and representation theory, Vol. 20, No. 5, 01.10.2017, p. 1109-1131.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Refinements of the Orthogonality Relations for Blocks
AU - Sambale, Benjamin
N1 - Publisher Copyright: © 2017, Springer Science+Business Media Dordrecht.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - For a block B of a finite group G there are well-known orthogonality relations for the generalized decomposition numbers. We refine these relations by expressing the generalized decomposition numbers with respect to an integral basis of a certain cyclotomic field. After that, we use the refinements in order to give upper bounds for the number of irreducible characters (of height 0) in B. In this way we generalize results from [Héthelyi-Külshammer-Sambale, 2014]. These ideas are applied to blocks with abelian defect groups of rank 2. Finally, we address a recent conjecture by Navarro.
AB - For a block B of a finite group G there are well-known orthogonality relations for the generalized decomposition numbers. We refine these relations by expressing the generalized decomposition numbers with respect to an integral basis of a certain cyclotomic field. After that, we use the refinements in order to give upper bounds for the number of irreducible characters (of height 0) in B. In this way we generalize results from [Héthelyi-Külshammer-Sambale, 2014]. These ideas are applied to blocks with abelian defect groups of rank 2. Finally, we address a recent conjecture by Navarro.
KW - Abelian defect groups
KW - k(B)
KW - Navarro Conjecture
KW - Orthogonality relations
UR - http://www.scopus.com/inward/record.url?scp=85014566862&partnerID=8YFLogxK
U2 - 10.1007/s10468-017-9676-1
DO - 10.1007/s10468-017-9676-1
M3 - Article
AN - SCOPUS:85014566862
VL - 20
SP - 1109
EP - 1131
JO - Algebras and representation theory
JF - Algebras and representation theory
SN - 1386-923X
IS - 5
ER -