Representations of Higher Adelic Groups and Arithmetic

Abstract

We discuss the following topics: n-dimensional local fields and adelic groups; harmonic analysis on local fields and adelic groups for two-dimensional schemes (function spaces, Fourier transform, Poisson formula); representations of discrete Heisenberg groups; adelic Heisenberg groups and their representations arising from two-dimensional schemes.

30 pages, to appear in Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010, vol. 1, corrected typos, added a reference

References in corpus (1)

• Harmonic analysis on local fields and adelic spaces I

Cited by in corpus (6)

• An introduction to higher dimensional local fields and adeles
• Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields
• Conjugacy classes in discrete Heisenberg groups
• On characterization of monomial representations of discrete supersolvable groups
• Central extensions and Riemann-Roch theorem on algebraic surfaces
• On monomial representations of finitely generated nilpotent groups