We consider the (extended) metaplectic representation of the semidirect product G=Hd⋊Sp(d,R) between the Heisenberg group and the symplectic group. Subgroups H=Σ⋊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 R2d or the wavelet representation of Rd⋊D, with D closed subgroup of GL(d,R). Finally, we shall provide new examples of reproducing groups of the type H=Σ⋊D, in dimension d=2.
Triangular subgroups of Sp(d,R) and reproducing formulae / Cordero, E.; Tabacco, Anita Maria. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 9:(2013), pp. 2034-2058. [10.1016/j.jfa.2013.02.004]
Triangular subgroups of Sp(d,R) and reproducing formulae
TABACCO, Anita Maria
2013
Abstract
We consider the (extended) metaplectic representation of the semidirect product G=Hd⋊Sp(d,R) between the Heisenberg group and the symplectic group. Subgroups H=Σ⋊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 R2d or the wavelet representation of Rd⋊D, with D closed subgroup of GL(d,R). Finally, we shall provide new examples of reproducing groups of the type H=Σ⋊D, in dimension d=2.Pubblicazioni consigliate
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https://hdl.handle.net/11583/2506440
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