Algebraic Structures on Virtual Characters of a Semisimple Lie Group

1988 ◽  
pp. 417-468
Author(s):  
Kyo Nishiyama
Keyword(s):  
Lie Group ◽  
Algebraic Structures ◽  
Semisimple Lie Group ◽  
Virtual Characters

INTEGRABILITY AND SYMMETRIC SPACES I: THE GROUP MANIFOLD

1989 ◽  
Vol 04 (03) ◽  
pp. 649-674 ◽  
Author(s):  
L. A. FERREIRA
Keyword(s):  
Poisson Bracket ◽  
Lie Group ◽  
Symmetric Spaces ◽  
Algebraic Structures ◽  
Semisimple Lie Group ◽  
Conserved Charges ◽  
Group Manifold ◽  
Coset Spaces

It is shown that any nonsingular Lagrangian describing the motion of a particle on a semisimple Lie group possesses a Fundamental Poisson bracket Relation (FPR) and consequently charges in involution. This property is independent of the dynamics of the model and can be derived in a quite simple and general way from the geometric and algebraic structures of the group manifold. The conditions a Hamiltonian has to satisfy in order those charges are to be conserved are discussed. These conditions lead to an algebra which plays an important role in the construction of conserved charges. In the second paper of the series, this work is extended to the coset spaces which are symmetric spaces.

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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