Degree Differences in the Eta Correspondences

Abstract

A sub-relation of the $\Theta$-correspondence called the \emph{$\eta$-correspondence} is defined by Gurevich-Howe for a finite reductive dual pair in stable range. In this paper we propose an extension of the correspondence to general finite reductive dual pairs. Then we determine the domain the correspondence and prove a formula on the difference of degrees in $q$ of two irreducible characters paired by the correspondence.

References in corpus (3)

• On Theta and Eta Correspondences for Finite Symplectic/Orthogonal Dual Pairs
• On Theta Ranks of Irreducible Characters of a Finite Classical Group
• On Theta and Eta Correspondences for Finite Unitary Dual Pairs