Geodesic
Vanishing Properties of Analytically Continued Matrix Coefficients
Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 409-421

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We consider (generalized) matrix coefficients associated to irreducible unitary representations of a simple Lie group G which admit holomorphic continuation to a complex semigroup domain S, subset of GC. Vanishing theorems for these analytically continued matrix coefficients, one of Howe-Moore type and one for cusp forms, are proved.
Classification : 22E46, 22A20, 22E40
Mots-clés : semisimple Lie group, highest weight representation, automorphic form, Olshanski semigroup, analytic continuation 
B. Krötz; M. Otto. Vanishing Properties of Analytically Continued Matrix Coefficients. Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 409-421. http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a5/
@article{JOLT_2002_12_2_a5,
     author = {B. Kr\"otz and M. Otto},
     title = {Vanishing {Properties} of {Analytically} {Continued} {Matrix} {Coefficients}},
     journal = {Journal of Lie Theory},
     pages = {409--421},
     year = {2002},
     volume = {12},
     number = {2},
     zbl = {1012.22027},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a5/}
}
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