The laplacian and the Dirac operator in infinitely many variables
The Last Possible Place of Unitarity for Certain Highest Weight Modules.
The Lefschetz Number of an Involution on the Space of Harmonic Cusp Forms of SL3.
The length spectrum of riemannian two-step nilmanifolds
The Lie algebra of a nuclear group.
The Lie group in infinite dimension.
The Lie group of real analytic diffeomorphisms is not real analytic
We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense of Milnor. ...
The linear symmetric systems associated with the modified Cherednik operators and applications
We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.
The Littlewood-Richardson rule - the cornerstone for computing group properties
The local theory of semigroups in nilpotent Lie groups.
The Mautner Phenomenon for p-adic Lie Groups.
The n-Homology of Harish-Chandra Modules: Generalizing a Theorem of Kostant.
The non-semi-simple term in the trace formula for rank one lattices.
The notion of norm and the representation theory of orthogonal groups.
The number of sides of a parallelogram.
The Oscillator Character Formula, for isometry groups of splits in deep stable range.
The outer automorphism group of normalizers of maximal tori in connected compact Lie groups.
The Perron product integral in Lie groups
The Plancherel theorem for general semisimple groups
The Poisson boundary of random rational affinities
We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all -adic fileds.