Homology, Homotopy and Applications

Volume 7 (2005)

Number 3

Proceedings of a Conference in honour of Victor Snaith

Explicit Brauer induction for symplectic and orthogonal representations

Pages: 99 – 153

DOI: https://dx.doi.org/10.4310/HHA.2005.v7.n3.a7

Authors

Olaf Neiße (Department of Computer & Electrical Engineering, University of Furtwangen, Germany)

Victor P. Snaith (Department of Pure Mathematics, University of Sheffield, United Kingdom)

Abstract

Explicit Brauer Induction formulae with certain natural behaviour have been developed for complex representations, for example by work of Boltje, Snaith and Symonds. In this paper we present induction formulae for symplectic and orthogonal representations of finite groups. The problems are motivated by number theoretical and topological questions. We will prove naturality with respect to restriction and inflation. Also we investigate complexification maps and use them to compare the orthogonal and symplectic induction formulae with Boltje’s complex induction formula.

Keywords

Brauer induction, symplectic representation

2010 Mathematics Subject Classification

20C15

Published 1 January 2005