there are dierent ways to code the geodesic flows on surfaces with negative curvature. such code spaces give a useful tool to verify the dynamical properties of geodesic flows. here we consider special subspaces of geodesic flows on hecke surface whose arithmetic codings varies on a set with in nite alphabet. then we will compare the topological complexity of them by computing their topologica...

There are dierent ways to code the geodesic flows on surfaces with negative curvature. Such code spaces give a useful tool to verify the dynamical properties of geodesic flows. Here we consider special subspaces of geodesic flows on Hecke surface whose arithmetic codings varies on a set with innite alphabet. Then we will compare the topological complexity of them by computing their topological ...

We study semi-classical limits of eigenfunctions of a quantized linear hyperbolic automorphism of the torus (" cat map "). For some values of Planck's constant, the spectrum of the quan-tized map has large degeneracies. Our first goal in this paper is to show that these degeneracies are coupled to the existence of quantum symmetries. There is a commutative group of unitary operators on the stat...

We study semi-classical limits of eigenfunctions of a quantized linear hyperbolic automorphism of the torus (“cat map”). For some values of Planck’s constant, the spectrum of the quantized map has large degeneracies. Our first goal in this paper is to show that these degeneracies are coupled to the existence of quantum symmetries. There is a commutative group of unitary operators on the state-s...

we consider a 2-dimensional representation of the hecke algebra h(g7; u), whereg7 is the complex re ection group and u is the set of indeterminatesu = (x1; x2; y1; y2; y3; z1; z2; z3):after specializing the indetrminates to non zero complex numbers, we then determine a nec-essary and sucient condition that guarantees the irreducibility of the complex specializationof the representation of the ...

We study the moduli surface for pairs of elliptic curves together with an isomorphism between their N-torsion groups. The Weil pairing gives a "determinant" map from this moduli surface to (Z/NZ)*; its fibres are the components of the surface. We define spaces of modular forms on these components and Hecke correspondences between them, and study how those spaces of modular forms behave as modul...

Hecke proved the meromorphic continuation of a Dirichlet series associated to the lattice points in a triangle with a real quadratic slope and found the possible poles in terms of the fundamental unit. An analogous result is proven for certain elliptical cones where now the poles are determined by the spectrum of the Laplacian on an arithmetic Riemann surface. 1 Some results of Hardy-Littlewood...

We show that the master equation governing the dynamics of simple diffusion and certain chemical reaction processes in one dimension give time evolution operators (Hamiltonians) which are realizations of Hecke algebras. In the case of simple diffusion one obtains, after similarity transformations, reducible hermitian representations while in the other cases they are non-hermitian and correspond...

We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine) Hecke-Clifford algebras of Olshanski and Jones-Nazarov. Relation between the spin (affine) Hecke algebra and a nonstandard presentation of the usual (affine) Hecke alge...