Related papers: Borel class and Cartan involution

Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has…

Let $\Sigma_{g,b}$ denote a closed oriented surface genus $g$ with $b$ punctures and let $Mod_{g,b}$ denote its mapping class group. Luo proved that if the genus is at least 3, the group $Mod_{g,b}$ is generated by involutions. He also…

Here a loop braid representation is a monoidal functor $\mathsf{F}$ from the loop braid category $\mathsf{L}$ to a suitable target category, and is $N$-charge-conserving if that target is the category $\mathsf{Match}^N$ of charge-conserving…

Let G = Aut(T) be the automorphism group of a regular tree T. We study continuous irreducible representations of G that preserve a continuous strongly nondegenerate sesquilinear form of finite index on a Hilbert space. These are already…

We establish an explicit bijection between the toric degenerations of the Grassmannian $\textrm{Gr}(2,n)$ arising from maximal cones in tropical Grassmannians and the ones coming from plabic graphs corresponding to $\textrm{Gr}(2,n)$. We…

This article proves that Tate classes on Siegel modular 3-folds are spanned by the images of Hilbert modular surfaces at degree 2 and by the images of Shimura curves at degree 4. The proof involves a careful study of the period pairing…

In this paper we prove a general theorem concerning the number of translation classes of curves of genus $g$ belonging to a fixed cohomology class in a polarized abelian variety of dimension $g$. For $g = 2$ we recover results of G\"ottsche…

We show that mod $2$ cohomological invariants of the moduli stack $\mathscr{M}_{3,n}$ of smooth pointed curves of genus three contain a free module with generators in degree $0$, $2$, $3$, $4$ and $6$, formed by the invariants of the…

We show that every Borel graph $G$ of subexponential growth has a Borel proper edge-coloring with $\Delta(G) + 1$ colors. We deduce this from a stronger result, namely that an $n$-vertex (finite) graph $G$ of subexponential growth can be…

We study the gerbal representations of a finite group $G$ or, equivalently, module categories over Ostrik's category $Vec_G^\alpha$ for a 3-cocycle $\alpha$. We adapt Bartlett's string diagram formalism to this situation to prove that the…

Let $G\subset\GL(\BC^r)$ be a finite complex reflection group. We show that when $G$ is irreducible, apart from the exception $G=\Sgot_6$, as well as for a large class of non-irreducible groups, any automorphism of $G$ is the product of a…

Let $G$ be a complex reductive group and $H=G^{\theta}$ be its fixed point subgroup under a Galois involution $\theta$. We show that any $H$-distinguished representation $\pi$ (i.e $\mathrm{dim}_{\mathbb{C}}\left(\pi^{*}\right)^{H}\neq0$)…

We give a new proof of the $k$-fold convolution of the Catalan numbers. This is done by enumerating a certain class of polygonal dissections called $k$-in-$n$ dissections. Furthermore, we give a formula for the average number of cycles in a…

We isolate a new preservation class of Suslin forcings and prove several associated consistency results in the choiceless theory ZF+DC regarding countable chromatic numbers of various Borel hypergraphs.

For a quantum group, we study those right coideal subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this property, then we call it a Borel subalgebra. Besides the…

In this paper we prove an Ax-Schanuel type result for the exponential functions for general linear groups over $\mathbb{C}$. We prove the result first for the group of upper triangular matrices and then for the group $GL_n$ of all $n\times…

A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…

We prove that the image of the mapping class group by the representations arising in the SU(2)-TQFT is infinite, provided that the genus is bigger than 2 and the level r of the theory is different from 2,3,4,6. In particular the quotient of…

We apply the equivariance --> families principle to a geometric family of Clifford module bundles with an action of a compact Lie group G to prove an equivariant version of Bismut's families index theorem on the differential Borel quotient…

Falbel, Koseleff and Rouillier computed a large number of boundary unipotent CR representations of fundamental groups of non compact three-manifolds. Those representations are not always discrete. By experimentally computing their limit…