A Construction of Representations of Weyl Groups.
A construction of unitary representations in parabolic rank two
A Distribution - Theoretic Proof of Kirillov's Character Formula for Nilpotent Lie Groups.
A generalization of the Enright-Varadarajan modules
A Geometric Construction of the Discrete Series for Semisimple Lie Groups.
A Proof of Blattner's Conjecture.
A reverse engineering approach to the Weil representation
We describe a new approach to the Weil representation attached to a symplectic group over a finite or a local field. We dissect the representation into small pieces, study how they work, and put them back together. This way, we obtain a reversed construction of that of T. Thomas, skipping most of the literature on which the latter is based.
A Stone-Weierstrass theorem for group representations.
Abelian simply transitive affine groups of symplectic type
The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. Similarly, we classify the complete global model spaces for flat special Kähler manifolds with a constant cubic form.
Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.
Allgemeine Lage und äquivariante Homotopie.
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.
Analysis in matrix space and Speh's representations.
Analysis on real affine -varieties.
Analytic continuation for Flensted-Jensen Representations.
Asymptotics of Matrix Coefficients, Perverse Sheaves and Jacquet Modules.
Berezin quantization and holomorphic representations
Berezin-Weyl quantization for Cartan motion groups
We construct adapted Weyl correspondences for the unitary irreducible representations of the Cartan motion group of a noncompact semisimple Lie group by using the method introduced in [B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177--190].
Bounding hyperbolic and spherical coefficients of Maass forms
We develop a new method to bound the hyperbolic and spherical Fourier coefficients of Maass forms defined with respect to arbitrary uniform lattices.