What are the important questions to start to study about Plancherel Formula for SL2? And what is the relation this topic and the Arthur's paper, "On some problems suggested by the trace formula (1984)" Can anyone suggest any source shows this relation?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
|
1
2
|
|
|
|
|
2
|
I can't speak to the second question, but a canonical source on Plancherel for $SL(2)$ is An Introduction to Harmonic Analysis on Semisimple Lie Groups V.S. Varadarajan |
||
|
|
You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.
|
7
|
Another standard reference for the Plancherel formula is the book: $SL_2(\mathbb{R})$, Addison-Wesley, 1974; of course $SL$ stands for Serge Lang. The Plancherel formula and the Selberg trace formula have in common that a trace is computed in two ways. But they deal with different representations of $G$. For $G$ a suitable locally compact group (type I, unimodular, separable), and $f\in C_c(G)$, the Plancherel formula is $f(e)=\int_{\hat{G}}Tr\pi(f)\;d\mu(\pi)$, where $\mu$ is the Plancherel measure on the dual $\hat{G}$; and the difficulty is, in concrete examples, to describe $\hat{G}$ and $\mu$ explicitly (or at least to describe explicitly the support of $\mu$, called the tempered dual). For the Selberg trace formula, I found the Wikipedia article fairly readable: http://en.wikipedia.org/wiki/Selberg_trace_formula |
|||
|
|
