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Conformally invariant trilinear forms on the sphere | | Jean-Louis Clerc
; Bent Orsted
; | | Date: |
16 Jan 2010 | | Abstract: | To each complex number $lambda$ is associated a representation $pi_lambda$
of the conformal group $SO_0(1,n)$ on $mathcal C^infty(S^{n-1})$ (spherical
principal series). For three values $lambda_1,lambda_2,lambda_3$, we
construct a trilinear form on $mathcal C^infty(S^{n-1}) imesmathcal
C^infty(S^{n-1}) imes mathcal C^infty(S^{n-1})$, which is invariant by
$pi_{lambda_1}otimes pi_{lambda_2}otimes pi_{lambda_3}$. The trilinear
form, first defined for $(lambda_1, lambda_2,lambda_3)$ in an open set of
$mathbb C^3$ is extended meromorphically, with simple poles located in an
explicit family of hyperplanes. For generic values of the parameters, we prove
uniqueness of trilinear invariant forms. | | Source: | arXiv, 1001.2851 | | Services: | Forum | Review | PDF | Favorites | |
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