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 consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$. After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of the repre...

In this paper we consider  (extended) metaplectic representation of the  semidirect product  $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$  where $mathbb{J}$ is a closed subgroup of $Sp(d,mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Fina...