TY - JOUR

T1 - Restriction of Odd Degree Characters and Natural Correspondences

AU - Giannelli, Eugenio

AU - Kleshchev, Alexander

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

N1 - Funding Information:
This work was supported by the European Research Council (ERC) Advanced [Grant 291512] to E.G.; National Science Foundation (NSF) [grant DMS-1161094] to A.K., the Fulbright Foundation (to A.K.), and the Max-Planck-Institut (to A.K.); Prometeo/Generalitat Valenciana, Proyectos MTM2013-40464-P to G.N.; NSF [grant DMS-1201374] to P.H.T.
Publisher Copyright:
© The Author(s) 2016. Published by Oxford University Press. All rights reserved.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

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U2 - 10.1093/imrn/rnw174

DO - 10.1093/imrn/rnw174

M3 - Article

AN - SCOPUS:85011402937

VL - 2017

SP - 6089

EP - 6118

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 20

ER -