An algebraic proof of the PRV conjecture for very regular weights.
An analogue of Hardy's theorem for the Heisenberg group
We observe that the classical theorem of Hardy on Fourier transform pairs can be reformulated in terms of the heat kernel associated with the Laplacian on the Euclidean space. This leads to an interesting version of Hardy's theorem for the sublaplacian on the Heisenberg group. We also consider certain Rockland operators on the Heisenberg group and Schrödinger operators on ℝⁿ related to them.
An analogue of the Weil representation for G2.
An application of the building to orbital integrals
An elementary approach to the hypergeometric shift operators of Opdam.
An Elementary Proof of the Baker-Campbell-Hausdorff-Dynkin Formula.
An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators.
An estimation of the controllability time for single-input systems on compact Lie Groups
Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters...
An example of Fourier transforms of orbital integrals and their endoscopic transfer.
An example of unipotent representations associated with a nilpotent nonminimal orbit: The case of orbits of dimension 10 of . (Un exemple de représentations unipotentes associées à une orbite nilpotente non minimale: le cas des orbites de dimension 10 de .)
An explicit computation of -stabilized vectors
In this paper, we give a concrete method to compute -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over -adic fields. An application to the global setting is also discussed. In particular, we give an explicit -stabilized form of a Saito-Kurokawa lift.
An explicit construction of the K-finite vectors in the discrete series for an isotropic semisimple symmetric space
An explicit construction of the metaplectic representation over a finite field.
An extension of Mahler's theorem to simply connected nilpotent groups
This Note gives an extension of Mahler's theorem on lattices in to simply connected nilpotent groups with a -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.
An extension of the Khinchin-Groshev theorem
We prove a version of the Khinchin-Groshev theorem in Diophantine approximation for quadratic extensions of function fields in positive characteristic.
An extention of Nomizu’s Theorem –A user’s guide–
For a simply connected solvable Lie group G with a lattice Γ, the author constructed an explicit finite-dimensional differential graded algebra A*Γ which computes the complex valued de Rham cohomology H*(Γ, C) of the solvmanifold Γ. In this note, we give a quick introduction to the construction of such A*Γ including a simple proof of H*(A*Γ) ≅ H*(Γ, C).
An F. and M. Riesz theorem for compact Lie groups.
An inequality for local unitary Theta correspondence
Given a representation of a local unitary group and another local unitary group , either the Theta correspondence provides a representation of or we set . If is fixed and varies in a Witt tower, a natural question is: for which is ? For given dimension there are exactly two isometry classes of unitary spaces that we denote . For let us denote the minimal of the same parity of such that , then we prove that where is the dimension of .
An infinite dimensional approach to the third fundamental theorem of Lie.
An integral formula for cocycles of Lie groups