Algèbre non commutative, groupes quantiques et invariants Septième contact Franco-Belge, Reims, Juin 1995
J. Alev, G. Cauchon (Éd.)
Séminaires et Congrès 2 (1997), 304 pages
Some Conjectures About Invariant Theory and their Applications
Séminaires et Congrès 2 (1997), 263-279
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It turns out that various algebraic computations can be reduced to the same type of computations: one has to study the series of integrals , where f,g are complex valued K-finite functions on a compact Lie group K. So it is tempting to state a general conjecture about the behavior of such integrals, and to investigate the consequences of the conjecture.
MAIN CONJECTURE : Let K be a compact connected Lie group and let f be a complex-valued K-finite function on K such that for any n> 0. Then for any K-finite function g, we have for n large enough.
Especially, we prove that the main conjecture implies the jacobian conjecture. Another very optimistic conjecture is proposed, and its connection to isospectrality problems is explained.
Class. math. : 14E07