Distinguished representations for SL(n,F)

Kwangho Choiy; Shiv Prakash Patel

doi:10.1016/j.jalgebra.2026.03.033

Distinguished representations for SL(n,F)

Kwangho Choiy
, Shiv Prakash Patel

Research output: Contribution to journal › Article › peer-review

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 SL_2n(F) by the subgroup H_♭:=SL_2n(F)∩GL_n(E), which is a variation of the work of Anandavardhanan and Prasad on distinguished representations of SL_n(E) by the subgroup SL_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 Hom_{H_♭}(π_♭,1) in terms of certain characters of F^×, where π_♭ is an irreducible representation which is also distinguished by H_♭.

Original language	English
Pages (from-to)	45-58
Number of pages	14
Journal	Journal of Algebra
Volume	701
DOIs	https://doi.org/10.1016/j.jalgebra.2026.03.033
State	Published - 1 Sep 2026
Externally published	Yes

Keywords

Branching laws
Distinguished representations of finite groups
Multiplicity formula

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jalgebra.2026.03.033

Cite this

@article{2e4dff4c8f7d4e5282209150a80a0408,

title = "Distinguished representations for SL(n,F)",

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 SL2n(F) by the subgroup H♭:=SL2n(F)∩GLn(E), which is a variation of the work of Anandavardhanan and Prasad on distinguished representations of SLn(E) by the subgroup SLn(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 HomH♭(π♭,1) in terms of certain characters of F{\texttimes}, where π♭ is an irreducible representation which is also distinguished by H♭.",

keywords = "Branching laws, Distinguished representations of finite groups, Multiplicity formula",

author = "Kwangho Choiy and Patel, \{Shiv Prakash\}",

note = "Publisher Copyright: {\textcopyright} 2026 Elsevier Inc.",

year = "2026",

month = sep,

day = "1",

doi = "10.1016/j.jalgebra.2026.03.033",

language = "English",

volume = "701",

pages = "45--58",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Distinguished representations for SL(n,F)

AU - Choiy, Kwangho

AU - Patel, Shiv Prakash

PY - 2026/9/1

Y1 - 2026/9/1

N2 - 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 SL2n(F) by the subgroup H♭:=SL2n(F)∩GLn(E), which is a variation of the work of Anandavardhanan and Prasad on distinguished representations of SLn(E) by the subgroup SLn(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 HomH♭(π♭,1) in terms of certain characters of F×, where π♭ is an irreducible representation which is also distinguished by H♭.

AB - 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 SL2n(F) by the subgroup H♭:=SL2n(F)∩GLn(E), which is a variation of the work of Anandavardhanan and Prasad on distinguished representations of SLn(E) by the subgroup SLn(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 HomH♭(π♭,1) in terms of certain characters of F×, where π♭ is an irreducible representation which is also distinguished by H♭.

KW - Branching laws

KW - Distinguished representations of finite groups

KW - Multiplicity formula

UR - https://www.scopus.com/pages/publications/105036739862

U2 - 10.1016/j.jalgebra.2026.03.033

DO - 10.1016/j.jalgebra.2026.03.033

M3 - Article

AN - SCOPUS:105036739862

SN - 0021-8693

VL - 701

SP - 45

EP - 58

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Distinguished representations for SL(n,F)

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this