Let $(J,\pi)$ be a cuspidal type in $SL(2,F)$, $F$ is a non-Arch. local field and let $I$ be the Iwahori subgroup of $SL(2,F)$. Is there any possibility that $J\subset I$ or even a subgroup?

I am working on the chamber homology for $SL(2,F)$, and stuck at some basic stuff on D.S. reps of $SL(2,F)$. Let $ I=\left( \begin{array}{cc} \mathcal{O}_{F} & \mathcal{O}_{F} \\ \varpi_{\mathbb{F}}\mathcal{O}_{F} & \mathcal{O}_{F}\\ \end{array} \right)\cap ...

I am looking for research that has been done in Discrete wavelets. Let me be specific as Google doesn't give me what I want when I say "discrete wavelets". I don't want countable basis for $ L^2(\mathbb{R}) $, Daubechies book, "Ten Lectures on Wavelets", already has this. I am looking for resear...

This function has been explored a bit at MSE (in June 2016): \begin{eqnarray} f(n) &=& (n-1)^2 \; \textrm{if} \; (n \bmod 4) = 1\\ f(n) &=& \lfloor n/4 \rfloor \; \textrm{otherwise} \end{eqnarray} with $f^k(n) = f(f( \cdots (n) \cdots ) )$ the result of applying $f(\;)$ $k$ times to $n$. The anal...

Goal. I would like to calculate the product of the formal dimension of a discrete series representation of $GL(2,\mathbb{Q}_p)$ with trivial central character (so, an irreducible unitary representation of $PGL(2,\mathbb{Q}_p)$ that is a subrepresentation of $L^2(PGL(2,\mathbb{Q}_p))$) and the c...

QUESTION Let $G$ be a simple Lie group with equal rank; namely, the rank of $G$ equals the rank of its maximal compact subgroup. Suppose that $G'$ is a reductive subgroup of $G$ with equal rank. If $\pi$ is a discrete series representation of $G$, is its restriction $\pi|_{G'}$ a discrete series...

I need to calculate the jitteriness for cyclic permutation from a set of finite discrete numbers. For example a sequence that does not change [1,1,1,1] would have the lowest possible value. The sequence that changes between the min and max value [0,9,0,9] would have highest possible value. A s...