# Unitarizable minimal principal series of reductive groups

**Authors:** Dan Barbasch, Dan Ciubotaru, Alessandra Pantano  
**arXiv:** [0804.1937](https://arxiv.org/abs/0804.1937)  
**Date:** 2008-04-11  
**Summary page:** https://www.summarizepaper.com/en/paper/0804.1937v1/

## Key points

- Recent advancements in determining unitarizable Langlands quotients of minimal principal series for reductive groups over real or p-adic fields
- Comprehensive overview of progress made in this area
- Langlands program seeks to establish connections between number theory and representation theory
- Focus on understanding Langlands correspondence, relating automorphic forms to Galois representations
- Specific focus on unitarizable Langlands quotients of minimal principal series
- Quotients play crucial role in representation theory of reductive groups over local fields
- Insights into irreducible representations and character formulas gained through study of these quotients
- Recent developments and results discussed, shedding light on properties and behavior
- Techniques and methodologies employed in determination explained
- Rigorous proofs and explanations provided for key results
- Addressing both real and p-adic fields extends applicability to different contexts
- Invaluable resource for researchers interested in representation theory of reductive groups over local fields

## Summary

This paper provides an in-depth exposition of the recent advancements made in determining the unitarizable Langlands quotients of minimal principal series for reductive groups over the real or p-adic fields in characteristic 0. The authors aim to present a comprehensive overview of the progress made in this area. The Langlands program is a fundamental research program that seeks to establish deep connections between number theory and representation theory. One important aspect of this program is understanding the Langlands correspondence, which relates automorphic forms on algebraic groups to representations of Galois groups. In this paper, the authors focus specifically on the unitarizable Langlands quotients of minimal principal series. These quotients play a crucial role in understanding the representation theory of reductive groups over local fields. By studying these quotients, one can gain insights into various aspects such as irreducible representations and character formulas. The paper highlights recent developments and results related to these unitarizable Langlands quotients. It discusses techniques and methodologies employed in their determination, shedding light on their properties and behavior. The authors provide rigorous proofs and explanations for key results, ensuring clarity and rigor in their presentation. Furthermore, the paper addresses both real and p-adic fields, extending its applicability to different contexts. This allows for a more comprehensive understanding of unitarizable Langlands quotients across various settings. Overall, this paper serves as an invaluable resource for researchers and mathematicians interested in the representation theory of reductive groups over local fields. Its detailed exposition of recent progress contributes significantly to advancing our knowledge and understanding of unitarizable Langlands quotients within characteristic 0.