Notes on Central Extensions

TL;DR

This paper provides an overview of central extensions and Schur multipliers, focusing on groups of Lie type over various fields, highlighting their structure and significance in representation theory.

Contribution

It offers a comprehensive lecture-based overview emphasizing the role of central extensions in groups of Lie type over different fields.

Findings

Clarifies the structure of central extensions in Lie groups

Highlights the importance of Schur multipliers in representation theory

Provides insights into the role of these concepts over finite, real, and p-adic fields

Abstract

These are the notes for some lectures given by this author at Harish-Chandra Research Institute, Allahabad in March 2014 for a workshop on Schur multipliers. The lectures aimed at giving an overview of the subject with emphasis on groups of Lie type over finite, real and $p$-adic fields.