TY - JOUR

T1 - On restriction of characters to defect groups

AU - Giannelli, Eugenio

AU - Sambale, Benjamin

N1 - Funding Information: The first author's research was funded by Trinity Hall, University of Cambridge. The second author is supported by the German Research Foundation (projects SA 2864/1-1 and SA 2864/3-1). Parts of this work were written while both authors participated at the conference Representations of Finite and Algebraic Groups at the MSRI Berkeley. The authors appreciate the financial support of the MSRI (NSF grant DMS-1440140).

PY - 2020/9/15

Y1 - 2020/9/15

N2 - We put forward a blockwise version of a recent conjecture of [6] on finite groups. Let B be a p-block of a finite group G with defect group D. Let χ∈Irr(B) be a character with positive height. In this note we conjecture that the number of distinct linear constituents of the restriction χD is 0 or at least p. We prove that this is indeed the case for various classes of finite groups and p-blocks.

AB - We put forward a blockwise version of a recent conjecture of [6] on finite groups. Let B be a p-block of a finite group G with defect group D. Let χ∈Irr(B) be a character with positive height. In this note we conjecture that the number of distinct linear constituents of the restriction χD is 0 or at least p. We prove that this is indeed the case for various classes of finite groups and p-blocks.

KW - Character restrictions

KW - Defect groups

UR - http://www.scopus.com/inward/record.url?scp=85070387294&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2019.07.011

DO - 10.1016/j.jalgebra.2019.07.011

M3 - Article

AN - SCOPUS:85070387294

VL - 558

SP - 423

EP - 433

JO - Journal of algebra

JF - Journal of algebra

SN - 0021-8693

ER -