Related papers: Fenchel-Nielsen coordinates for SL(3,C) representa…

For the base field of complex numbers we discuss the relationship between categories of coherent sheaves on compact Riemann surfaces and categories of coherent sheaves on weighted smooth projective curves. This is done by bringing back to…

Let F be a local non-archimedean field and let G be the group of F-valued points of a reductive algebraic group over F. In this paper we compute the Ext-groups of generalized Steinberg representations in the category of smooth…

We consider the space $F_n$ of configurations of $n$ points in $P^2$ satisfying the condition that no three of the points lie on a line. For $n = 4, 5, 6$, we compute $H^*(F_n; \mathbb{Q})$ as an $S_n$-representation. The cases $n = 5, 6$…

Let ${\mathbb{F}_{q}}$ be the finite field of order $q$. Let $G$ be one of the three groups ${\rm GL}(n, \mathbb{F}_q)$, ${\rm SL}(n, \mathbb{F}_q)$ or ${\rm U}(n, \mathbb{F}_q)$ and let $W$ be the standard $n$-dimensional representation of…

We characterize the representations of the fundamental group of a closed surface to $\mathrm{PSL}_2(\mathbb C)$ that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the…

With the $[0,1,2]$-family of cyclic triangulations we introduce a rich class of vertex-transitive triangulations of surfaces. In particular, there are infinite series of cyclic $q$-equivelar triangulations of orientable and non-orientable…

We classify representations of the mapping class group of a surface of genus $g$ (with at most one puncture or boundary component) up to dimension $3g-3$. Any such representation is the direct sum of a representation in dimension $2g$ or…

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

We propose a generalisation of the Jacquet-Langlands correspondence to the whole Grothendieck group of finite lenght admissible representations. As an application we prove some particular cases of the global Jacquet-Langlands…

We find an explicit presentation of relative linear Steinberg groups $\mathrm{St}(n, R, I)$ for any ring $R$ and $n \geq 4$ by generators and relations as abstract groups. We also prove a similar result for relative simply laced Steinberg…

Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index 1.

These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3, C). Expanding upon existing techniques, we stratify the space of representations and compute the E-polynomial of each geometrically…

The initial descriptions of the FITS format provided a simplified method for describing the physical coordinate values of the image pixels, but deliberately did not specify any of the detailed conventions required to convey the complexities…

We will compute the stable upper genus for the family of finite non-abelian simple groups $PSL_2(\mathbb{F}_p)$ for $p \equiv 3~(mod~4)$. This classification is well-grounded in the other branches of Mathematics like topology, smooth, and…

We characterise the quotient surface graphs arising from symmetric contact systems of line segments in the plane and also from symmetric pointed pseudotriangulations in the case where the group of symmetries is generated by a translation or…

In this paper, we compute the characters of the simple supercuspidal representations of SL(2,F) and SL(3,F) on split tori. Here, F is an arbitrary non-Archimedean local field of characteristic zero.

We consider the discrete representations of 3-manifold groups into $PU(2,1)$ that appear in the Falbel-Koseleff-Rouillier census, such that the peripheral subgroups have cyclic unipotent holonomy. We show that two of these representations…

We define a class of representations of the fundamental group of a closed surface of genus $2$ to $\mathrm{PSL}_2 (\mathbb C)$: the pentagon representations. We show that they are exactly the non-elementary $\mathrm{PSL}_2 (\mathbb…

Let $F$ be a non archimedean local field of characteristic zero, we give a classification of generic representations of $GL(n,F)$ distinguished by a maximal Levi subgroup, in terms of inducing discrete series.