Discrete Heisenberg-Weyl Group and Modular Group

Abstract

It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers $\theta$ and $-1/\theta$ generate the whole algebra $\mathcal{B}$ of bounded operators on $L_2(\mathbf{R})$. The natural action of the modular group in $\mathcal{B}$ is implied. Applications to dynamical algebras appearing in lattice regularization and some duality principles are discussed.

12 pages, LaTeX file

References in corpus (1)

• Abelian Current Algebra and the Virasoro Algebra on the Lattice

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