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.
2013
264
9
2034
2058
http://arxiv.org/pdf/1402.4604v1.pdf
http://dx.doi.org/10.1016/j.jfa.2013.02.004
metaplectic representation; semidirect product; Heisenberg group; symplectic group
E. Cordero; A. Tabacco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/128121
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