Induced Representations on Character Varieties of Surfaces

TL;DR

This paper demonstrates that a Frobenius reciprocity map on surface character varieties acts as a Poisson embedding, revealing new geometric structures in the study of surface representations.

Contribution

It establishes a Poisson embedding property of the Frobenius reciprocity map on character varieties, linking representation theory and Poisson geometry.

Findings

Frobenius reciprocity map is a Poisson embedding

Connects representation theory with Poisson geometry

Provides new insights into surface character varieties

Abstract

We show that a Frobenius reciprocity map on character varieties of surfaces is a Poisson embedding.