Algebras of entire functions and representations of the twisted Heisenberg group

Sundaram Thangavelu ()
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Sundaram Thangavelu: Indian Institute of Science

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 3, 911-921

Abstract: Abstract On the twisted Fock spaces $$ \mathcal {F}^\lambda ({\mathbb {C}}^{2n}) $$ F λ ( C 2 n ) we consider a family of unitary operators $$\rho _\lambda (a,b) $$ ρ λ ( a , b ) indexed by $$ (a,b) \in {\mathbb {C}}^n \times {\mathbb {C}}^n.$$ ( a , b ) ∈ C n × C n . The composition formula for $$ \rho _\lambda (a,b) \circ \rho _\lambda (a^\prime ,b^\prime ) $$ ρ λ ( a , b ) ∘ ρ λ ( a ′ , b ′ ) leads us to a group $$ \mathbb {H}^n_\lambda ({\mathbb {C}}) $$ H λ n ( C ) which contains two copies of the Heisenberg group $$ \mathbb {H}^n.$$ H n . The operators $$ \rho _\lambda (a,b) $$ ρ λ ( a , b ) lift to $$ \mathbb {H}_\lambda ^n({\mathbb {C}}) $$ H λ n ( C ) providing an irreducible unitary representation. However, its restriction to $$ \mathbb {H}^n_\lambda (\mathbb {R}) $$ H λ n ( R ) is not irreducible.

Keywords: Heisenberg groups; Fock spaces; Unitary representations; Banach algebras (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-024-00636-x

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