1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations
A 2-dimensional Algebraic Variety With 27 Rectilinear Generators and 108 Trisecants and its Connection With the Maximal Exceptional Simple lie Group
A Borel-Weil theorem for holomorphic forms
A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform
In this note, we generalize the results in our previous paper on the Casimir operator and Berezin transform, by showing the -continuity of a generalized Berezin transform associated with a branching problem for a class of unitary representations defined by invariant elliptic operators; we also show, that under suitable general conditions, this generalized Berezin transform is -continuous for
A classification of multiplicity free representations.
A comparison theorem for -homology
A complete analogue of Hardy's theorem on semisimple Lie groups
A result by G. H. Hardy ([11]) says that if f and its Fourier transform f̂ are and respectively for some m,n ≥ 0 and α > 0, then f and f̂ are and respectively for some polynomials P and P’. If in particular f is as above, but f̂ is , then f = 0. In this article we will prove a complete analogue of this result for connected noncompact semisimple Lie groups with finite center. Our proof can be carried over to the real reductive groups of the Harish-Chandra class.
A connected complex simple centerfree Lie group whose exponential function is not surjective.
A construction of unitary representations in parabolic rank two
A constructive approach to tensor product decompositions.
A duality between and . (Une dualité entre et .)
A geometric embedding for standard analytic modules.
A method for weight multiplicity computation based on Berezin quantization.
A Multiplicity One Theorem for Holomorphically Induced Representations.
A Note on Continuous Cohomology for Semisimple Lie Groups.
A note on Lie semialgebras in .
A note on parabolic subgroups.
A note on the linear cycle space for groups of Hermitian type.
A remarkable contraction of semisimple Lie algebras
Recently, E.Feigin introduced a very interesting contraction of a semisimple Lie algebra (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of . For instance, the algebras of invariants of both adjoint and coadjoint representations of are free, and also the enveloping algebra of is a free module over its centre.
A saturation property for powers of irreducible characters.