The $-_+$ and $-^+$ constructions for biset functors

TL;DR

This paper introduces the $-_+$ and $-^+$ constructions within biset functors, enabling the development of canonical induction formulas for various representation rings and unifying their study.

Contribution

It extends the $-_+$ and $-^+$ constructions to biset functors, providing a framework for canonical induction formulas and unifying several important functors.

Findings

Framework for canonical induction formulas for biset functors

Unified approach to Burnside, monomial Burnside, and global representation rings

Enhanced understanding of functor constructions in representation theory

Abstract

In this article we define the $-_+$-construction and the $-^+$-construction, that was crucial in the theory of canonical induction formulas (see \cite{Boltje1998b}), in the setting of biset functors, thus providing the necessary framework to define and construct canonical induction formulas for representation rings that are most naturally viewed as biset functors. Additionally, this provides a unified approach to the study of a class of functors including the Burnside ring, the monomial Burnside ring and global representation ring.