# Introduction to Representations of Real Semisimple Lie Groups

@article{Libine2012IntroductionTR, title={Introduction to Representations of Real Semisimple Lie Groups}, author={Matvei Libine}, journal={arXiv: Representation Theory}, year={2012} }

These are lecture notes for a one semester introductory course I gave at Indiana University. The goal was to make this exposition as clear and elementary as possible. A particular emphasis is given on examples involving SU(1,1). These notes are in part based on lectures given by my graduate advisor Wilfried Schmid at Harvard University and PQR2003 Euroschool in Brussels as well as other sources.

## 3 Citations

### Lie Group Machine Learning and Gibbs Density on Poincaré Unit Disk from Souriau Lie Groups Thermodynamics and SU(1, 1) Coadjoint Orbits

- MathematicsGSI
- 2019

Souriau method could be applied on Lie Groups to define a covariant maximum entropy density by Kirillov representation theory and illustrated for homogeneous Siegel domains and more especially for Poincare unit disk by considering SU(1,1) group coadjoint orbit and by using its Souriau’s moment map.

### Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation

- MathematicsEntropy
- 2020

A new geometric definition of Entropy is proposed that could be built as a generalized Casimir invariant function in coadjoint representation, and Massieu characteristic function, dual of Ent entropy by Legendre transform, is proposed.

### Probing holography in $p$-adic CFT

- Mathematics
- 2019

We holographically calculate the partition functions of CFTs dual to Bruhat-Tits trees and $p$-adic BTZ black holes. Along the way, we propose new spectral decompositions of the Laplacian operator…

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