5 problems

Let $V$ be an $n$-dimensional vector space, and let ${\rm CB}(V)$ be the simplicial complex whose simplices are collections of proper non-zero subspaces of $V$ with a common basis.…

Let $V$ be a finite-dimensional vector space over a field $k$. Let ${\mathcal{PD}}(V)$ be the poset of non-empty partial decompositions of $V$, ordered by refinement, and let…

A Moufang foundation is a foundation in which the irreducible rank $2$ buildings are Moufang and the glueings are compatible with the Moufang structures induced on the rank $1$ res…

Let two twin buildings be $2$-spherical, and consider a local isometry between them. Tits's extension conjecture. The extension theorem for local isometries should generalize to…

Let $F$ be a non-archimedean local field, let $G={\rm GL}(N,F)$ with $N\geq 2$, and let $\pi$ be a smooth complex representation of $G$ lying in the Bernstein block $\cal B(\pi)$ o…