Distinguished representations for \rmSL(n,F)

2025/11/15 by Kwangho Choiy, Choiy, Kwangho, Shiv Prakash Patel +1
Mathematics · #11F70 #20G25 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2511.12299

openalex publication_date 2025/11/15 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28

Abstract

Let F be a finite field, and let 𝔼 be either a quadratic field extension E/F or the split algebra F ⊕ F. We study distinguished representations of \rmSL_2n(F) by the subgroup H_\flat := \rmSL_2n(F) ∩ \rmGL_n(𝔼), which is a variation of the work of Anandavardhanan and Prasad on distinguished representations of \rmSL_n(𝔼) by the subgroup \rmSL_n(F). This is in a similar framework of our earlier work of a p-adic non-split variation of Anandavardhanan-Prasad over finite fields. We give a formula for the dimension of the complex vector space \rmHom_H_\flat(π_\flat, 1) in terms of certain characters of F^×, where π_\flat is an irreducible representation which is also distinguished by H_\flat.

Citations

• Multiplicity one for the pair (GL(n,D),GL(n,E))
• Multiplicities under basechange: finite field case
• Distinguished representations for SL(n)

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