On Theta and Eta Correspondences for Finite Symplectic/Orthogonal Dual Pairs

Abstract

In this paper, we propose two maximal one-to-one sub-relations $\underline{\theta },\overline{\theta }$ of the Howe correspondence $\Theta$ for a finite reductive dual pair consisting of a symplectic group and an orthogonal group. Moreover, we show that both the correspondences $\underline{\theta }$ and $\overline{\theta }$ are extensions beyond the stable range of the $\eta$-correspondence defined by Gurevich-Howe.

References in corpus (2)

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

Cited by in corpus (5)

• Howe Correspondence of Unipotent Characters for a Finite Symplectic/Even-orthogonal Dual Pair
• On Theta Ranks of Irreducible Characters of a Finite Classical Group
• On Theta and Eta Correspondences for Finite Unitary Dual Pairs
• Correspondences between affine Hecke algebras and applications
• Degree Differences in the Eta Correspondences