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Extra resources for Harmonic Analysis: Proceedings of a Conference Held at the University of Minnesota, Minneapolis, April 20–30, 1981

Sample text

Admissible is representation Hermitian nondefinite wPw -I = 0P; if 26 is irreducible, then it is not infinitesimally unitary. 4. Sufficiency of studying cases with real infinitesimal character. theorem: In unpublished work Vogan has proved the following Any irreducible unitary representation with nonreal infinitesimal character is of the form ind~N(~@ where MAN is a proper parabolic unitary representation of e i~ eih@ M i) , subgroup, ~ is an irreducible with real infinitesimal character, is a unitary character of A.

A m e r . J. M a t h . 82, 1 9 1 - 2 1 2 (1960). [2] C o l i n C. G r a h a m a n d O. C a r r u t h M c G e h e e , E s s a y s in C o m m u t a t i v e H a r m o n i c A n a l y s i s . New York-Heidelberg-Berlin: s p r i n g e r 1979. [3] G. H. H a r d y a n d J. E. L i t t l e w o o d , A n e w p r o o f o f a theorem on rearrangements. J. L o n d o n M a t h . Soc. 23, 1 6 3 - 1 6 8 (1948). [4] J. P. K a h a n e a n d Y. K a t z n e l s o n , H o m e o m o r p h m s m e s du c e r c l e et s e r m e s de F o u r i e r absolu_ment c o n v e r g e n t e s .

48 (1947), 568-640. 3. A. Borel and N. Wallach, "Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups," Ann. of Math. Studies 94, Princeton Univ. Press, Princeton, NJ, ~ . 4. M. Duflo, Representations unitaires irrSductibles des groupes simples complexes de rang deux, Bull. Soc. Math. France 107 (1979), 55-96. 5. M. Duflo, Repr$sentations unitaires des groupes semi-simples complexes, "Group-Theoretical Methods in Physics," Ann. Israel Phys. Soc. 3 (1980), 19-34. 6.

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