We show that intertwining operators for the discrete Fourier transform form a cubic algebra Cq, with q being root of unity. This is intimately related to other two well-known realizations algebra: Askey–Wilson and Askey–Wilson–Heun algebra.

For locally compact groups, Fourier algebras and Fourier-Stieltjes algebras have proved to be useful dual objects. They encode the representation theory of the group via the positive deenite functions on the group: positive deenite functions correspond to cyclic representations and span these algebras as linear spaces. They encode information about the algebra of the group in the geometry of th...

We provide necessary and sufficient conditions for the existence of idempotents arbitrarily large norm in Fourier algebra $A(G)$ Fourier–Stieltjes $B(G)$ a locally compact group $G$. prove that

The paper is mainly based on the series of lectures on the onedimensional double Hecke algebra delivered by the first author at Harvard University in 2001. It also contains the material of other talks (MIT, University Paris 6) and new results. The most interesting is the classification of finite-dimensional representations. Concerning the proofs, we followed the principle the more proof the bet...

We show that the biflatness—in the sense of A. Ya. Helemskĭı—of the Fourier algebra A(G) of a locally compact groupG forcesG to either have an abelian subgroup of finite index or to be non-amenable without containing F2 as a closed subgroup. An analogous dichotomy is obtained for biprojectivity.

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.