Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On the symmetric square: definitions and lemmas


Author: Yuval Z. Flicker
Journal: Trans. Amer. Math. Soc. 330 (1992), 111-124
MSC: Primary 11F70; Secondary 22E50
MathSciNet review: 1041046
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We define the symmetric square lifting for admissible and automorphic representations, from the group $ H = {H_0} = {\text{SL}}(2)$, to the group $ G = {\text{PGL}}(3)$, and derive its basic properties. This lifting is defined by means of Shintani character relations. The definition is suggested by the computation of orbital integrals (stable and unstable) in our On the symmetric square: Orbital integrals, Math. Ann. 279 (1987), 173-193. It is compatible with dual group homomorphisms $ {\lambda _0}:\widehat{H} \to \widehat{G}$ and $ {\lambda _1}:{\widehat{H}_1} \to \widehat{G}$, where $ {H_1} = {\text{PGL}}(2)$. The lifting is proven for induced, trivial and special representations, and both spherical functions and orthogonality relations of characters are studied.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 11F70, 22E50

Retrieve articles in all journals with MSC: 11F70, 22E50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1041046-2
PII: S 0002-9947(1992)1041046-2
Article copyright: © Copyright 1992 American Mathematical Society