Kronecker positivity and 2-modular representation theory

verfasst von

Christine Bessenrodt, Christopher Bowman, Louise Sutton

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

University of York
Okinawa Institute of Science and Technology Graduate University (OIST)

Typ

Artikel

Journal

Transactions of the American Mathematical Society. Series B

Band

8

Seiten

1024-1055

Anzahl der Seiten

32

ISSN

2330-0000

Publikationsdatum

10.12.2021

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (sonstige)

Elektronische Version(en)

https://doi.org/10.48550/arXiv.1903.07717 (Zugang: Offen)
https://doi.org/10.1090/btran/70 (Zugang: Offen)