TY - JOUR

T1 - On the symmetric square

T2 - Definitions and lemmas

AU - Flicker, Yuval Z.

N1 - Publisher Copyright:
© 1992 American Mathematical Society.

PY - 1992

Y1 - 1992

N2 - We define the symmetric square lifting for admissible and automorphic representations, from the group H = H0 = SL(2), to the group G = 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 λo: Ĥ —>Ĝ and λ1 : Ĥ1 —► Ĝ, where H1 = PGL(2). The lifting is proven for induced, trivial and special representations, and both spherical functions and orthogonality relations of characters are studied.

AB - We define the symmetric square lifting for admissible and automorphic representations, from the group H = H0 = SL(2), to the group G = 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 λo: Ĥ —>Ĝ and λ1 : Ĥ1 —► Ĝ, where H1 = PGL(2). The lifting is proven for induced, trivial and special representations, and both spherical functions and orthogonality relations of characters are studied.

UR - http://www.scopus.com/inward/record.url?scp=84916157305&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1992-1041046-2

DO - 10.1090/S0002-9947-1992-1041046-2

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AN - SCOPUS:84916157305

SN - 0002-9947

VL - 330

SP - 111

EP - 124

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 1

ER -