Local descent to quasi-split even general spin groups

Eyal Kaplan; Jing Feng Lau; Baiying Liu

doi:10.1007/s00209-023-03227-4

Local descent to quasi-split even general spin groups

Eyal Kaplan, Jing Feng Lau, Baiying Liu

Department of Mathematics

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

Abstract

Let n> 1 and let τ be an irreducible unitary supercuspidal representation of GL ₂_n over a local non-archimedean field. Assuming the twisted symmetric square L-function of τ has a pole at s= 0 , we construct the local descent of τ to the corresponding quasi-split even general spin group GSpin ₂_n. We prove this local descent is generic, unitary, supercuspidal and multiplicity free. Its irreducible quotients are “functorially related” to τ, in the analytic sense of a pole of a Rankin–Selberg type γ-function.

Original language	English
Article number	69
Journal	Mathematische Zeitschrift
Volume	303
Issue number	3
DOIs	https://doi.org/10.1007/s00209-023-03227-4
State	Published - Mar 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

This research was supported by the ISRAEL SCIENCE FOUNDATION Grant nos. 376/21 and 421/17 (Kaplan), and by NSF Grants DMS-1702218, DMS-1848058, and start-up funds from the Department of Mathematics at Purdue University (Liu).

Funders	Funder number
Department of Mathematics at Purdue University
National Science Foundation	DMS-1848058, DMS-1702218
Israel Science Foundation	421/17, 376/21

Keywords

GSpin groups
Local Langlands functoriality
Local descent

Access to Document

10.1007/s00209-023-03227-4

Cite this

@article{69bd7a2e0d6e41919bbf81fa0a0f6dce,

title = "Local descent to quasi-split even general spin groups",

abstract = "Let n> 1 and let τ be an irreducible unitary supercuspidal representation of GL 2n over a local non-archimedean field. Assuming the twisted symmetric square L-function of τ has a pole at s= 0 , we construct the local descent of τ to the corresponding quasi-split even general spin group GSpin 2n. We prove this local descent is generic, unitary, supercuspidal and multiplicity free. Its irreducible quotients are “functorially related” to τ, in the analytic sense of a pole of a Rankin–Selberg type γ-function.",

keywords = "GSpin groups, Local Langlands functoriality, Local descent",

author = "Eyal Kaplan and Lau, {Jing Feng} and Baiying Liu",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2023",

month = mar,

doi = "10.1007/s00209-023-03227-4",

language = "אנגלית",

volume = "303",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Local descent to quasi-split even general spin groups

AU - Kaplan, Eyal

AU - Lau, Jing Feng

AU - Liu, Baiying

PY - 2023/3

Y1 - 2023/3

N2 - Let n> 1 and let τ be an irreducible unitary supercuspidal representation of GL 2n over a local non-archimedean field. Assuming the twisted symmetric square L-function of τ has a pole at s= 0 , we construct the local descent of τ to the corresponding quasi-split even general spin group GSpin 2n. We prove this local descent is generic, unitary, supercuspidal and multiplicity free. Its irreducible quotients are “functorially related” to τ, in the analytic sense of a pole of a Rankin–Selberg type γ-function.

AB - Let n> 1 and let τ be an irreducible unitary supercuspidal representation of GL 2n over a local non-archimedean field. Assuming the twisted symmetric square L-function of τ has a pole at s= 0 , we construct the local descent of τ to the corresponding quasi-split even general spin group GSpin 2n. We prove this local descent is generic, unitary, supercuspidal and multiplicity free. Its irreducible quotients are “functorially related” to τ, in the analytic sense of a pole of a Rankin–Selberg type γ-function.

KW - GSpin groups

KW - Local Langlands functoriality

KW - Local descent

UR - http://www.scopus.com/inward/record.url?scp=85148765700&partnerID=8YFLogxK

U2 - 10.1007/s00209-023-03227-4

DO - 10.1007/s00209-023-03227-4

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85148765700

SN - 0025-5874

VL - 303

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3

M1 - 69

ER -

Local descent to quasi-split even general spin groups

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this