Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1024-1055 |
| Seitenumfang | 32 |
| Fachzeitschrift | Transactions of the American Mathematical Society. Series B |
| Jahrgang | 8 |
| Ausgabenummer | 33 |
| Publikationsstatus | Veröffentlicht - 10 Dez. 2021 |
Abstract
This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these results and other modular representation theoretic techniques on the study of Kronecker coefficients and hence verify Saxl’s conjecture for several large new families of partitions. In particular, we verify Saxl’s conjecture for all irreducible characters of S n which are of 2-height zero.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Mathematik (sonstige)
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in: Transactions of the American Mathematical Society. Series B, Jahrgang 8, Nr. 33, 10.12.2021, S. 1024-1055.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Kronecker positivity and 2-modular representation theory
AU - Bessenrodt, Christine
AU - Bowman, Christopher
AU - Sutton, Louise
N1 - Funding Information: Received by the editors August 2, 2019, and, in revised form, September 2, 2020. 2020 Mathematics Subject Classification. Primary 05E10, 20C30. The second author would like to thank both the Alexander von Humboldt Foundation and the Leibniz Universität Hannover for financial support and an enjoyable summer. The third author was supported by Singapore MOE Tier 2 AcRF MOE2015-T2-2-003.
PY - 2021/12/10
Y1 - 2021/12/10
N2 - This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these results and other modular representation theoretic techniques on the study of Kronecker coefficients and hence verify Saxl’s conjecture for several large new families of partitions. In particular, we verify Saxl’s conjecture for all irreducible characters of S n which are of 2-height zero.
AB - This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these results and other modular representation theoretic techniques on the study of Kronecker coefficients and hence verify Saxl’s conjecture for several large new families of partitions. In particular, we verify Saxl’s conjecture for all irreducible characters of S n which are of 2-height zero.
UR - http://www.scopus.com/inward/record.url?scp=85135810092&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1903.07717
DO - 10.48550/arXiv.1903.07717
M3 - Article
VL - 8
SP - 1024
EP - 1055
JO - Transactions of the American Mathematical Society. Series B
JF - Transactions of the American Mathematical Society. Series B
SN - 2330-0000
IS - 33
ER -