On the symmetric square: Twisted trace formula

Yuval Z. Flicker

doi:10.1016/0022-1236(91)90095-M

On the symmetric square: Twisted trace formula

Yuval Z. Flicker

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We compute a trace formula-for a test function on PGL(3,A)- twisted by the outer automorphism σ(g)=J^tg^-1J, J= 0 1 1 1 0 The resulting formula is then compared with trace formulae for H = H₀0 = SL(2) and H₁ = PGL(2), and matching functions f₀ and f₁ thereof. We obtain a trace formula identity which plays a key role in our study of the symmetric square lifting from H(A) to G(A). Our formulae are remarkably simple, due to the introduction of a new concept of a regular function. This eliminates the singular and weighted integrals in the trace formulae.

Original language	English
Pages (from-to)	194-210
Number of pages	17
Journal	Journal of Functional Analysis
Volume	98
Issue number	1
DOIs	https://doi.org/10.1016/0022-1236(91)90095-M
State	Published - 15 May 1991
Externally published	Yes

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abstract = "We compute a trace formula-for a test function on PGL(3,A)- twisted by the outer automorphism σ(g)=Jtg-1J, J= 0 1 1 1 0 The resulting formula is then compared with trace formulae for H = H00 = SL(2) and H1 = PGL(2), and matching functions f0 and f1 thereof. We obtain a trace formula identity which plays a key role in our study of the symmetric square lifting from H(A) to G(A). Our formulae are remarkably simple, due to the introduction of a new concept of a regular function. This eliminates the singular and weighted integrals in the trace formulae.",

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N2 - We compute a trace formula-for a test function on PGL(3,A)- twisted by the outer automorphism σ(g)=Jtg-1J, J= 0 1 1 1 0 The resulting formula is then compared with trace formulae for H = H00 = SL(2) and H1 = PGL(2), and matching functions f0 and f1 thereof. We obtain a trace formula identity which plays a key role in our study of the symmetric square lifting from H(A) to G(A). Our formulae are remarkably simple, due to the introduction of a new concept of a regular function. This eliminates the singular and weighted integrals in the trace formulae.

AB - We compute a trace formula-for a test function on PGL(3,A)- twisted by the outer automorphism σ(g)=Jtg-1J, J= 0 1 1 1 0 The resulting formula is then compared with trace formulae for H = H00 = SL(2) and H1 = PGL(2), and matching functions f0 and f1 thereof. We obtain a trace formula identity which plays a key role in our study of the symmetric square lifting from H(A) to G(A). Our formulae are remarkably simple, due to the introduction of a new concept of a regular function. This eliminates the singular and weighted integrals in the trace formulae.

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On the symmetric square: Twisted trace formula

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