Suppose \(G\) is a real reductive algebraic group, \(\theta\) is an automorphism of \(G\), and \(\omega\) is a quasicharacter of the group of real points \(G(\mathbf{R})\). Under some additional assumptions, the theory of twisted endoscopy associates to this triple real reductive groups \(H\). The Local Langlands Correspondence partitions the admissible representations of \(H(\mathbf{R})\) and \(G(\mathbf{R})\) into \(L\)-packets. The author proves twisted character identities between \(L\)-packets of \(H(\mathbf{R})\) and \(G(\mathbf{R})\) comprised of essential discrete series or limits of discrete series.

Table of Contents

• Introduction
• Notation
• The foundations of real twisted endoscopy
• The Local Langlands Correspondence
• Tempered essentially square-integrable representations
• Spectral transfer for essentially square-integrable representations
• Spectral transfer for limits of discrete series
• Appendix A. Parabolic descent for geometric transfer factors
• Bibliography
• Index