Details
Originalsprache | Englisch |
---|---|
Aufsatznummer | 107184 |
Fachzeitschrift | Advances in mathematics |
Jahrgang | 369 |
Frühes Online-Datum | 13 Mai 2020 |
Publikationsstatus | Veröffentlicht - 5 Aug. 2020 |
Abstract
Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such a classification is known when the characteristic of the ground field is greater than 3, but the small characteristics cases require a substantially more delicate analysis and new ideas. Our results fit into the Aschbacher-Scott program on maximal subgroups of finite classical groups.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Advances in mathematics, Jahrgang 369, 107184, 05.08.2020.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Irreducible restrictions of representations of symmetric and alternating groups in small characteristics
AU - Kleshchev, Alexander
AU - Morotti, Lucia
AU - Tiep, Pham Huu
N1 - Funding Information: The first author was supported by the NSF grant DMS-1700905 and the DFG Mercator program through the University of Stuttgart . The second author was supported by the DFG grant MO 3377/1-1 and the DFG Mercator program through the University of Stuttgart . The third author was supported by the NSF (grants DMS-1839351 and DMS-1840702 ), and the Joshua Barlaz Chair in Mathematics . This work was also supported by the NSF grant DMS-1440140 and Simons Foundation while all three authors were in residence at the MSRI during the Spring 2018 semester.
PY - 2020/8/5
Y1 - 2020/8/5
N2 - Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such a classification is known when the characteristic of the ground field is greater than 3, but the small characteristics cases require a substantially more delicate analysis and new ideas. Our results fit into the Aschbacher-Scott program on maximal subgroups of finite classical groups.
AB - Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such a classification is known when the characteristic of the ground field is greater than 3, but the small characteristics cases require a substantially more delicate analysis and new ideas. Our results fit into the Aschbacher-Scott program on maximal subgroups of finite classical groups.
KW - Alternating groups
KW - Irreducible restrictions
KW - Modular representations
KW - Symmetric groups
UR - http://www.scopus.com/inward/record.url?scp=85084394114&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2020.107184
DO - 10.1016/j.aim.2020.107184
M3 - Article
VL - 369
JO - Advances in mathematics
JF - Advances in mathematics
SN - 0001-8708
M1 - 107184
ER -