On the local coefficients matrix for coverings of SL2

Fan Gao; Freydoon Shahidi; Dani Szpruch

doi:https://doi.org/10.1007/978-3-319-97379-1_10

On the local coefficients matrix for coverings of SL₂

Fan Gao, Freydoon Shahidi, Dani Szpruch

Mathematics discipline

Open University of Israel

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We discuss the Gelfand–Kazhdan criterion for covering groups with abelian covering tori and also investigate several aspects of the local coefficients matrix for genuine principal series representations of coverings of SL₂. The goal is to carry out some preliminary study on some invariants attached to the local coefficients matrix, with a view toward a theory of γ -factors and L-functions for genuine representations of covering groups.

Original language	English
Title of host publication	Springer Proceedings in Mathematics and Statistics
Pages	207-244
Number of pages	38
DOIs	https://doi.org/10.1007/978-3-319-97379-1_10
State	Published - 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	251

Keywords

Covering groups
Gamma factor
Gelfand–Kazhdan criterion
Local coefficients matrix
Metaplectic groups
Plancherel measure
Whittaker functionals

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1007/978-3-319-97379-1_10

Cite this

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KW - Plancherel measure

KW - Whittaker functionals

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