Let $F$ be a local field of characteristic zero and $G$ a connected reductive group over $F$. Let us call an inducing datum a triple $(P,M,\sigma)$, where $P$ is a parabolic subgroup of $G$, $M$ is a Levi factor of $P$, and $\sigma$ is an irreducible admissible representation of $M(F)$. Let $I_{M...

(I'd like to premise that I'm not an expert about these topics (just a student), so many of my doubts and perplexities are probably symptoms of my mathematical immaturity) I'm currently studying differentiable stacks and I'm a little confused by the following statement: Many classes of interesti...

As it was shown by Malcev, unlike the commutative case, in which every domain can be embedded in a field, there are noncommutative domains that can't be embedded in a division ring. For noncommutative domains, the nicest way they can be embedded in a division ring is if they satisfie Ore's condit...

Motivation. The starting point of this question is the trivial observation that if we cover $\mathbb{N}$ with $$\big\{\{0,\ldots n\}: n\in \mathbb{N}\big\},$$ then this cover doesn't have a minimal subcover (from which no more sets can be taken away). So in this question we focus on covers in whi...

It is known that for a primitive substitution $S:\mathcal{A}\to \mathcal{A}^+$, there exists constants $c,C>0$ such that $$ c\theta_S^n \leq \vert S^n(a)\vert \leq C \theta_S^n \quad \text{for all} \; a\in \mathcal{A} \quad \text{and} \; n\in \mathbb{N}, $$ where $\theta_S$ is the Perron-Frobeni...

There are $N \geq 1$ white balls and $1$ black ball in an (infinitely big) urn. Every turn, a ball is drawn from the urn uniformly at random. If a white ball is drawn, it is put back into the urn along with one more white ball. If a black ball is drawn, it is put back into the urn along with two ...