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 (5)

• Howe Correspondence of Unipotent Characters for a Finite Symplectic/Even-orthogonal Dual Pair
• Lusztig Correspondence and Howe Correspondence for Finite Reductive Dual Pairs
• 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