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