Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields

TL;DR

This paper investigates how the Heisenberg group acts on distribution spaces associated with two-dimensional local fields, providing insights into the structure and representations of these mathematical objects.

Contribution

It introduces a natural action of the Heisenberg group on distribution spaces of two-dimensional local fields, expanding understanding of their representation theory.

Findings

Characterization of the Heisenberg group's action on distribution spaces

New insights into the structure of two-dimensional local fields

Potential applications to algebraic geometry and number theory

Abstract

We study a natural action of the Heisenberg group of integer unipotent matrices of the third order on distribution space of a two-dimensional local field for a flag on a two-dimensional scheme.