Restriction of Odd Degree Characters and Natural Correspondences

Eugenio Giannelli, Alexander Kleshchev, Gabriel Navarro, Pham Huu Tiep

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Let q be an odd prime power, n > 1, and let P denote a maximal parabolic subgroup of GLn (q) with Levi subgroup GLn-1 (q) × GL1 (q). We restrict the odd-degree irreducible characters of GLn (q) to P to discover a natural correspondence of characters, both for GLn (q) and SLn (q). A similar result is established for certain finite groups with self-normalizing Sylow p-subgroups. Next, we construct a canonical bijection between the odd-degree irreducible characters of G = Sn, GLn (q) or GUn (q) with q odd, and those of NG(P), where P is a Sylow 2-subgroup of G. Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that the fields of values of character correspondents are the same. We use this to answer some questions of R. Gow.

Original languageEnglish (US)
Pages (from-to)6089-6118
Number of pages30
JournalInternational Mathematics Research Notices
Volume2017
Issue number20
DOIs
StatePublished - Oct 1 2017

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Restriction of Odd Degree Characters and Natural Correspondences'. Together they form a unique fingerprint.

  • Cite this