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
DOI:
https://doi.org/10.1090/S0002-9947-1992-1041046-2
MathSciNet review:
1041046
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Abstract | References | Similar Articles | Additional Information
Abstract: We define the symmetric square lifting for admissible and automorphic representations, from the group , to the group
, 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
and
, where
. The lifting is proven for induced, trivial and special representations, and both spherical functions and orthogonality relations of characters are studied.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1992-1041046-2
Article copyright:
© Copyright 1992
American Mathematical Society