An analogue of the Weil representation for G2.
An analytic series of irreducible representations of the free group
Let be a free group on generators. We construct the series of uniformly bounded representations of acting on the common Hilbert space, depending analytically on the complex parameter z, , such that each representation is irreducible. If is real or then is unitary; in other cases cannot be made unitary. For representations and are congruent modulo compact operators.
An application of Lie groupoids to a rigidity problem of 2-step nilmanifolds
We study a problem of isometric compact 2-step nilmanifolds using some information on their geodesic flows, where is a simply connected 2-step nilpotent Lie group with a left invariant metric and is a cocompact discrete subgroup of isometries of . Among various works concerning this problem, we consider the algebraic aspect of it. In fact, isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, namely by normalizers. So, suitable factorization...
An application of peripherality to compact semigroups.
An application of the building to orbital integrals
An associated mob of a topological group.
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 a generalized completely continuous representation of a locally compact group
There is constructed a compactly generated, separable, locally compact group G and a continuous irreducible unitary representation π of G such that the image π(C*(G)) of the group C*-algebra contains the algebra of compact operators, while the image of the -group algebra does not containany nonzero compact operator. The group G is a semidirect product of a metabelian discrete group and a “generalized Heisenberg group”.
An Example of a Non Nuclear C*-Algebra, which has the Metric Approximation Property.
An Example of a Q-minimal Precompact Topological Group Containing a Nonminimal Closed Normal Subgroup.
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 Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups
We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schrödinger operators obtained in this...
An extension of a theorem of F. Forelli.