Question

From the book Lorentz group and harmonic analysis of Ruhl, in particular I'm interest in chapter 5 and 6. I'm a master students Give some resources (notes, books ...) to start with. The topics are:

The representation theory of SL(2,R)
, in particular to find all the unitary irreducible repr. of it. (discrete series, principal and complementary)
The harmonic analysis on this group

Answer 1

For a comprehensive study on the representation theory of SL(2,R) and harmonic analysis, I recommend starting with "Representation Theory: A First Course" by William Fulton and Joe Harris. Additionally, "Harmonic Analysis on Semisimple Lie Groups" by V.S. Varadarajan provides a solid foundation for the harmonic analysis aspects.

Step-by-step explanation:

To delve deeper into the specific topics of discrete series, principal, and complementary unitary irreducible representations, you may find "Harmonic Analysis on Reductive p-adic Groups" by Robert Herb and Andrea Maffei useful. This book delves into the representation theory of p-adic groups, offering insights applicable to SL(2,R) as well.

Exploring the recommended books as starting points for mastering the representation theory of SL(2,R) and harmonic analysis on semisimple Lie groups.

Question:

I am a master's student focusing on the Lorentz group and harmonic analysis, particularly in chapters 5 and 6 of Ruhl's book. I am interested in the representation theory of SL(2,R), specifically in finding all the unitary irreducible representations, including discrete series, principal, and complementary ones, as well as delving into harmonic analysis on this group. Can you provide resources such as notes or books to start my study in these areas?