On naturally reductive left-invariant metrics of SL (2, R)

INVARIANT GENERALIZED FUNCTIONS ON sl(2,R) WITH VALUES IN A sl(2,R)-MODULE

Let g be a finite dimensional real Lie algebra. Let ρ : g → End(V ) be a representation of g in a finite dimensional real vector space. Let CV = ( End(V )⊗S(g) )g be the algebra of End(V )-valued invariant differential operators with constant coefficients on g. Let U be an open subset of g. We consider the problem of determining the space of generalized functions φ on U with values in V which a...

6 Ratner ’ S Theorem on Sl ( 2 , R ) - Invariant Measures

We give a relatively short and self contained proof of Ratner’s theorem in the special case of SL(2, R)-invariant measures.

Symmetry preserving discretization of SL(2,R) invariant equations

Symmetry preserving discretization of SL(2,R) invariant equations Anne Bourlioux a, Raphaël Rebelo b,c and Pavel Winternitz a,b a Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, Québec H3C 3J7, Canada. E-mail: [email protected] b Centre de recherches mathématiques, Université de Montréal, C.P. 6128, succ. Centre-ville, Mon...

Analysis on SL ( 2 ) Representations of SL 2 ( R )

This essay is about representations. It says nothing about what might be called invariant harmonic analysis on G. It does not discuss orbital integrals at all, and says very little about characters. Nor does it prove anything deep about the relationship between representations of G and those of its Lie algebra, or about versions of Fourier transforms. These topics involve too much analysis to b...

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