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Towards the Jacquet conjecture on the Local Converse Problem for p -adic GL n

Dihua Jiang, Chufeng Nien, Shaun Stevens (2015)

Journal of the European Mathematical Society

The Local Converse Problem is to determine how the family of the local gamma factors γ ( s , π × τ , ψ ) characterizes the isomorphism class of an irreducible admissible generic representation π of GL n ( F ) , with F a non-archimedean local field, where τ runs through all irreducible supercuspidal representations of GL r ( F ) and r runs through positive integers. The Jacquet conjecture asserts that it is enough to take r = 1 , 2 , ... , n 2 . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture,...

Transitive riemannian isometry groups with nilpotent radicals

C. Gordon (1981)

Annales de l'institut Fourier

Given that a connected Lie group G with nilpotent radical acts transitively by isometries on a connected Riemannian manifold M , the structure of the full connected isometry group A of M and the imbedding of G in A are described. In particular, if G equals its derived subgroup and its Levi factors are of noncompact type, then G is normal in A . In the special case of a simply transitive action of G on M , a transitive normal subgroup G ' of A is constructed with dim G ' = dim G and a sufficient condition is given...

Triangular stochastic matrices generated by infinitesimal elements

Inheung Chon, Hyesung Min (1999)

Czechoslovak Mathematical Journal

We show that each element in the semigroup S n of all n × n non-singular upper (or lower) triangular stochastic matrices is generated by the infinitesimal elements of S n , which form a cone consisting of all n × n upper (or lower) triangular intensity matrices.

Troisième théorème fondamental de réalisation de Cartan

Ngô van Quê, A.A.M. Rodrigues (1975)

Annales de l'institut Fourier

De même qu’avec les groupes de Lie, à tout pseudo-groupe infinitésimal de Lie θ sur R n il est associé de façon naturelle une algèbre de Lie L ( θ ) , qui est une sous-algèbre de Lie fermée de l’algèbre de Lie D de tous les champs de vecteurs formels de R n , l’algèbre D étant munie de la topologie définie par la filtration naturelle de l’algèbre des séries formelles. Le troisième théorème fondamental de Cartan dit qu’inversement étant donnée une sous-algèbre de Lie transitive fermée L de l’algèbre D , il existe...

Truncated Lie groups and almost Klein models

Georges Giraud, Michel Boyom (2004)

Open Mathematics

We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M G. Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup.

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