We consider the (extended) metaplectic representation of the semidirect product between the Heisenberg group and the symplectic group. Subgroups H = Σ x D, with Σ being a d × d symmetric matrix and D a closed subgroup of GL(d,R), are our main concern. We shall give a general setting for the reproducibility of such groups which include and assemble the ones for the single examples treated in Cordero et al. (2006) [4]. As a byproduct, the extended metaplectic representation restricted to some classes of such subgroups is either the Schrödinger representation of R^2d or the wavelet representation of R^d x D, with D closed subgroup of GL(d,R). Finally, we shall provide new examples of reproducing groups of the type H = Σ x D, in dimension d = 2.
Triangular subgroups of Sp(d,R) and reproducing formulae
CORDERO, Elena;
2013-01-01
Abstract
We consider the (extended) metaplectic representation of the semidirect product between the Heisenberg group and the symplectic group. Subgroups H = Σ x D, with Σ being a d × d symmetric matrix and D a closed subgroup of GL(d,R), are our main concern. We shall give a general setting for the reproducibility of such groups which include and assemble the ones for the single examples treated in Cordero et al. (2006) [4]. As a byproduct, the extended metaplectic representation restricted to some classes of such subgroups is either the Schrödinger representation of R^2d or the wavelet representation of R^d x D, with D closed subgroup of GL(d,R). Finally, we shall provide new examples of reproducing groups of the type H = Σ x D, in dimension d = 2.File | Dimensione | Formato | |
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