Kronecker positivity and 2-modular representation theory

authored by

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Univ. York, Dep. Comput. Sci., Non-Stand. Comput. Group
Okinawa Institute of Science and Technology Graduate University (OIST)

Type

Article

Journal

Transactions of the American Mathematical Society. Series B

Volume

8

Pages

1024-1055

No. of pages

32

ISSN

2330-0000

Publication date

10.12.2021

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics (miscellaneous)

Electronic version(s)

https://doi.org/10.48550/arXiv.1903.07717 (Access: Open)
https://doi.org/10.1090/btran/70 (Access: Open)