Related papers: Automorphisms of character varieties

In positive characteristic, algebraic curves can have many more automorphisms than expected from the classical Hurwitz's bound. There even exist algebraic curves of arbitrary high genus g with more than 16g^4 automorphisms. It has been…

Let O be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite O-module M of rank two. The main emphasis is on the interaction between…

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…

The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key…

We prove new automorphy lifting theorems for residually reducible Galois representations of unitary type in which the residual representation is permitted to have an arbitrary number of irreducible constituents.

We give a description of several representation varieties of the fundamental group of the complement of the figure eight knot in PGL(3,C) or SL(3,C). We moreover obtain an explicit parametrization of matrices generating the representation…

This is a common introduction to math.RT/0101170, math.RT/0306333, math.RT/0506043, math.RT/0601028. Compared to these references there are new results including (i) a description of a separable closure of an extension of transcendence…

We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be…

In this note, we prove that if every character of a finite group $G$ fixed by an order-2 Galois automorphism has odd degree, then $G$ has a normal Sylow $2$-subgroup. On the way, we study extensions of characters of $GL_n(q)$, $q$ odd, to…

We first give a relative flexible process to construct torsion cohomology classes for Shimura varieties of Kottwitz-Harris-Taylor type with coefficient in a non too regular local system. We then prove that associated to each torsion…

The aim of this article is to study the SL(2,C)-character scheme of a finitely generated group. Given a presentation of a finitely generated group $\Gamma$, we give equations defining the coordinate ring of the scheme of SL(2,C)-characters…

We show that Mukai's classification of finite groups which may act symplectically on a complex K3 surface extends to positive characteristic $p$ under the assumptions that (i) the order of the group is coprime to $p$ and (ii) either the…

This article presents a 3-local characterisation of the sporadic simple group McL and its automorphism group. The theorem is underpinned by a further identification theorem the proof of which is character theoretic. The main theorem is…

Let $G$ be a finite group acting on a connected compact surface $\Sigma$, and $M$ be an integer homology 3-sphere. We show that if each element of $G$ is extendable over $M$ with respect to a fixed embedding $\Sigma\rightarrow M$, then $G$…

We describe the geometry of the character variety of representations of the knot group $\Gamma_{m,n}=\langle x,y| x^n=y^m\rangle$ into the group $\mathrm{SU}(3)$, by stratifying the character variety into strata correspoding to totally…

For any complex affine reductive group G and a fixed choice of maximal compact subgroup K, we show that the G-character variety of a free group strongly deformation retracts to the corresponding K-character space, which is a real…

This paper gives insight into intriguing connections between two apparently unrelated theories: the theory of skein modules of 3-manifolds and the theory of representations of groups into special linear groups of 2 by 2 matrices. Let R be a…

This is the second of a series of papers which aim towards a classification of edge-transitive maps of which the Euler characteristic and the edge number are coprime. This one carries out the classification work for arc-transitive maps with…

We study the group of automorphisms of the affine plane preserving some given curve, over any field. The group is proven to be algebraic, except in the case where the curve is a bunch of parallel lines. Moreover, a classification of the…

We prove that the group of automorphisms of the Lie algebra $\Der_K (P_n)$ of derivations of a polynomial algebra $P_n=K[x_1,..., x_n]$ over a field of characteristic zero is canonically isomorphic to the the group of automorphisms of the…