Howe Correspondence of Unipotent Characters for a Finite Symplectic/Even-orthogonal Dual Pair

2019/01/03 by Shu-Yen Pan, Pan, Shu-Yen · 5 citations
Mathematics · #20C33 #22E50 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1901.00623

openalex publication_date 2019/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a complete description of the Howe correspondence of unipotent characters for a finite dual pair of a symplectic group and an even orthogonal group in terms of the Lusztig parametrization under a mild restriction of the characteristic of the base field. That is, the conjecture by Aubert-Michel-Rouquier is confirmed.

Citations

• Decomposition of the Uniform Projection of the Weil Character

Cited by

• On the Howe correspondence and Harish-Chandra series
• Correspondences between affine Hecke algebras and applications
• On Theta and Eta Correspondences for Finite Symplectic/Orthogonal Dual Pairs
• On Theta and Eta Correspondences for Finite Unitary Dual Pairs
• Degree Differences in the Eta Correspondences

Related

• Lusztig Correspondence and Howe Correspondence for Finite Reductive Dual Pairs
• Decomposition of the Uniform Projection of the Weil Character
• Howe duality over finite fields I: The two stable ranges
• A note on the Howe Duality conjecture for symplectic-orthogonal and unitary pairs
• On Theta and Eta Correspondences for Finite Symplectic/Orthogonal Dual Pairs