For a locally compact group G, let A(G) denote its Fourier algebra and Ĝ its dual object, i.e. the collection of equivalence classes of unitary representations of G. We show that the amenability constant of A(G) is less than or equal to sup{deg(π) : π ∈ Ĝ} and that it is equal to one if and only if G is abelian.

Let W be a finite group generated by unitary reflections and A be the set of reflecting hyperplanes. We will give a characterization of the logarithmic differential forms with poles along A in terms of antiinvariant differential forms. If W is a Coxeter group defined over R, then the characterization provides a new method to find a basis for the module of logarithmic differential forms out of b...

Let W be a nite group generated by unitary re ections and A be the set of re ecting hyperplanes. We will give a characterization of the logarithmic di erential forms with poles along A in terms of antiinvariant di erential forms. If W is a Coxeter group de ned over R, then the characterization provides a new method to nd a basis for the module of logarithmic di erential forms out of basic invar...

Let $$\pi $$ be a non-self-dual unitary cuspidal automorphic representation not of solvable polyhedral type for $$\mathrm{GL}(2)$$ over number field. We show that has positive upper Dirichlet density Hecke eigenvalues in any sector whose angle is at least 2.63 radians.

We derive a precise relation of poles Eisenstein series associated to the cuspidal datum $\chi\otimes\sigma$ and lowest occurrence theta lifts automorphic representation $\sigma$ unitary group, where $\chi$ is conjugate self-dual character. A key ingredient proof computation period integrals truncated series.

In Part I of this thesis, we locate a (conjecturally complete) set of unitary representations in the admissible dual of U(p, q). In a little more detail, Barbasch and Vogan have used the theory of Kazhdan-Lusztig cells to parametrize the irreducible Harish-Chandra modules with integral infinitesimal character in terms of their annihilators and associated varieties. Vogan has conjectured that th...

The classical duality theory associates to an abelian locally compact group a dual companion. Passing to a non-abelian group, a dual object can still be defined, but it is no longer a group. The search for a broader category which should include both the groups and their duals, points towards the concept of quantization. Classically, the regular representation of a group contains the complete i...

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfan...