Smooth Fréchet globalizations of Harish-Chandra modules
By J. Bernstein, Bernhard Krötz. 2008
139 citations recorded by the source corpus.
We give an alternative proof of the Casselman-Wallach globalization theorem. The approach is based on lower bounds for matrix coefficients on a reductive group.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1aa55d417fab101411f1547fa6837a82a2c59ea6
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Multiplicity one theorems: the Archimedean case (2009, background): “Fr´echet, smooth, of moderate growth, admissible and Z-finite. Here Z is the center of the universal enveloping algebra of its complexified Lie algebra. The reader may consult [Ca], [W2, Chapter 11] or [BK] for more details about Casselman-Wallach representations. By (a version of) the Gelfand-Kazhdan”
- The nonvanishing hypothesis at infinity for Rankin-Selberg convolutions (2013, background): “ve group is called a Casselman-Wallach representation if it is smooth, Fr´echet, of moderate growth, and its Harish-Chandra module has finite length. The reader may consult [Cas], [Wa2, Chapter 11] or [BK] for details about Casselman-Wallach representations. As is quite common, we do not distinguish ”