The duality theorems. Cyclic representations Langlands conjectures

Janusz Szmidt

GDML_Books, (1980), p.

Résumé

CONTENTSIntroduction...................................................................................................... 5Chapter I. Invariant kernels on locally compact groups and cyclicrepresentations....................................................................................................... 8 1. Distributions on topological groups.......................................... 8 2. Invariant kernels and cyclic representations.................................... 9 3. Generalized cyclic vectors. An extension of the Gelfand-Raikov correspondence......................................................................................... 12 4. Cyclicity of induced representations.................................................. 15Chapter II. Duality theorems for induced representationswith elliptic differential operator............................................................................. 17 1. Induced representations............................................................... 17 2. Invariant differential operators.............................................................. 19 3. The general duality theorem for induced representations.............. 20 4. Duality theorems with elliptic differential operator............................ 22 5. The case where G/Γ is not compact.................................................... 30Chapter III. The duality theorem and Langlands conjectures................. 30 1. The discrete series representations........................................... 31 2. The Langlands conjectures.................................................................. 32Chapter IV. Dirac operator and the discrete classes.Hotta and Parthasarathy theorem......................................................................... 30 1. Dirac operator.................................................................................. 39 2. The realization of the discrete series representations.................... 42 3. The multiplicity theorem......................................................................... 45References........................................................................................................ 46

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EUDML-ID : urn:eudml:doc:268507