On adelic model of boson Fock space. (English) Zbl 1173.11356
Neretin, Yu. (ed.) et al., Moscow Seminar in mathematical physics, II. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4371-0/hbk). Translations. Series 2. American Mathematical Society 221. Advances in the Mathematical Sciences 60, 193-202 (2007).
Summary: We construct a canonical embedding of the Schwartz space on \(\mathbb R^n\) to the space of distributions on the adelic product of all the \(p\)-adic numbers. This map is equivariant with respect to the action of the symplectic group \(\mathrm{Sp}(2n, \mathbb Q)\) over rational numbers and with respect to the action of rational Heisenberg group.
These notes contain two elements. First, we give a funny realization of a space of complex functions of a real variable as a space of functions of \(p\)-adic variable. Secondly, we try to clarify the classical construction of modular forms through \(\theta\)-functions and Howe duality
For the entire collection see [Zbl 1124.58002].
These notes contain two elements. First, we give a funny realization of a space of complex functions of a real variable as a space of functions of \(p\)-adic variable. Secondly, we try to clarify the classical construction of modular forms through \(\theta\)-functions and Howe duality
For the entire collection see [Zbl 1124.58002].
MSC:
| 11R56 | Adèle rings and groups |
| 81S05 | Commutation relations and statistics as related to quantum mechanics (general) |
| 11F27 | Theta series; Weil representation; theta correspondences |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
| 46S10 | Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis |
