Boundary and Eisenstein Cohomology of $G_2(\mathbb{Z})$

TL;DR

This paper computes the Eisenstein cohomology of the arithmetic group G_2(Z) with various coefficients by analyzing the boundary cohomology of its Borel-Serre compactification.

Contribution

It provides a detailed determination of Eisenstein cohomology for G_2(Z) with arbitrary finite-dimensional highest weight coefficients, advancing understanding of automorphic forms.

Findings

Explicit description of Eisenstein cohomology for G_2(Z)

Analysis of boundary cohomology via Borel-Serre compactification

Extension of cohomological methods to exceptional groups

Abstract

In this article, Eisenstein cohomology of the arithmetic group $G_2(\mathbb{Z})$ with coefficients in any finite dimensional highest weight irreducible representation has been determined. We accomplish this by studying the cohomology of the boundary of the Borel-Serre compactification.