Let G be a finite group, and g â‰¥ 2. We study the locus of genus g curves that admit a G-action of given type, and inclusions between such loci. We use this to study the locus of genus g curves withâ€¦ (More)

Let G be a split simply laced group defined over a p-adic field F . In this paper we study the restriction of the minimal representation of G to various dual pairs in G. For example, the restrictionâ€¦ (More)

We investigate the question when the tensor square, the alternating square, or the symmetric square of an absolutely irreducible projective representation V of an almost simple group G is againâ€¦ (More)

Let Cg be a general curve of genus g â‰¥ 4. Guralnick and others proved that the monodromy group of a cover Cg â†’ P 1 of degree n is either Sn or An. We show that An occurs for n â‰¥ 2g + 1. Theâ€¦ (More)

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and theâ€¦ (More)

If a black box group is known to be isomorphic to an exceptional simple group of Lie type of (twisted) rank > 1, other than any F4(q), over a field of known size, a Las Vegas algorithm is given toâ€¦ (More)

Let G be a finite group. By Riemannâ€™s Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy groupâ€¦ (More)

Corollary 1.2 Let G be an almost simple classical group with natural module V of dimension n. If G is linear, assume that G does not contain a graph automorphism. Let 2 â‰¤ k < n âˆ’ 1, and let K be theâ€¦ (More)

Article history: Received 29 April 2014 Available online 17 September 2014 Communicated by Charles Leedham-Green MSC: primary 20D06, 20G40 secondary 20B40, 20G41, 20P05, 68Q25