scholarly journals Invariant eigendistributions on a semisimple Lie group

1965 ◽  
Vol 119 (3) ◽  
pp. 457-457 ◽  
Author(s):  
Harish-Chandra
Keyword(s):  
Lie Group ◽  
Semisimple Lie Group

On Limit Multiplicities for Spaces of Automorphic Forms

1999 ◽  
Vol 51 (5) ◽  
pp. 952-976 ◽  
Author(s):  
Anton Deitmar ◽  
Werner Hoffmann
Keyword(s):  
Lie Group ◽  
Automorphic Forms ◽  
Plancherel Measure ◽  
Semisimple Lie Group ◽  
Selberg Trace Formula ◽  
Arithmetic Subgroup ◽  
Trivial Group ◽  
Rank One ◽  
Discrete Part ◽  
Cocompact Lattices

AbstractLet Γ be a rank-one arithmetic subgroup of a semisimple Lie group G. For fixed K-Type, the spectral side of the Selberg trace formula defines a distribution on the space of infinitesimal characters of G, whose discrete part encodes the dimensions of the spaces of square-integrable Γ-automorphic forms. It is shown that this distribution converges to the Plancherel measure of G when Γ shrinks to the trivial group in a certain restricted way. The analogous assertion for cocompact lattices Γ follows from results of DeGeorge-Wallach and Delorme.

scholarly journals ON THE EXACTNESS OF KOSTANT–KIRILLOV FORM AND THE SECOND COHOMOLOGY OF NILPOTENT ORBITS

2012 ◽  
Vol 23 (08) ◽  
pp. 1250086 ◽  
Author(s):  
INDRANIL BISWAS ◽  
PRALAY CHATTERJEE
Keyword(s):  
Lie Algebra ◽  
Lie Group ◽  
Nilpotent Orbits ◽  
Semisimple Lie Group ◽  
Simple Lie Algebra ◽  
Adjoint Orbits ◽  
Adjoint Orbit

We give a criterion for the Kostant–Kirillov form on an adjoint orbit in a real semisimple Lie group to be exact. We explicitly compute the second cohomology of all the nilpotent adjoint orbits in every complex simple Lie algebra.

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