Let U(q) be a Sylow p-subgroup of the Chevalley groups D4(q) where q is a power of a prime p. We describe a construction of all complex irreducible characters of U(q) and obtain a classification of these irreducible characters via the... more
Let U(q) be a Sylow p-subgroup of the Chevalley groups D4(q) where q is a power of a prime p. We describe a construction of all complex irreducible characters of U(q) and obtain a classification of these irreducible characters via the root subgroups which are contained in the center of these characters. Furthermore, we show that the multiplicities of the degrees of these irreducible characters are given by polynomials in (q−1) with nonnegative integer coefficients.
We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt(5) and SL_2(5) is a Beauville group. In particular, we settle a... more
We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt(5) and SL_2(5) is a Beauville group. In particular, we settle a conjecture of Bauer, Catanese and Grunewald which asserts that all non-abelian finite simple groups except for the alternating group Alt(5) are Beauville groups.
Let q be a power of a prime p, let G be a finite Chevalley group over F q and let U be a Sylow p-subgroup of G; we assume that p is not a very bad prime for G. We explain a procedure of reduction of irreducible complex characters of U ,... more
Let q be a power of a prime p, let G be a finite Chevalley group over F q and let U be a Sylow p-subgroup of G; we assume that p is not a very bad prime for G. We explain a procedure of reduction of irreducible complex characters of U , which leads to an algorithm whose goal is to obtain a parametrization of the irreducible characters of U along with a means to construct these characters as induced characters. A focus in this paper is determining the parametrization when G is of type F 4 , where we observe that the parametrization is "uniform" over good primes p > 3, but differs for the bad prime p = 3. We also explain how it has been applied for all groups of rank 4 or less.
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We describe a new algorithm for computing braid orbits on Nielsen classes. As an application we classify all families of affine genus zero systems; that is all families of coverings of the Riemann sphere by itself such that the monodromy... more
We describe a new algorithm for computing braid orbits on Nielsen classes. As an application we classify all families of affine genus zero systems; that is all families of coverings of the Riemann sphere by itself such that the monodromy group is a primitive affine permutation group.
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Let C_g be a general curve of genus g>3. Guralnick and others proved that the monodromy group of a cover C_g-> P^1 of degree n is either S_n or A_n. We show that A_n occurs for n>2g. The corresponding result for S_n is classical.
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ABSTRACT In this paper we analyze the structure of transitive permutation groups that have trivial four point stabilizers, but some nontrivial three point stabilizer. In particular we give a complete, detailed classification when the... more
ABSTRACT In this paper we analyze the structure of transitive permutation groups that have trivial four point stabilizers, but some nontrivial three point stabilizer. In particular we give a complete, detailed classification when the group is simple or quasisimple. This paper is motivated by questions concerning the relationship between fixed points of automorphisms of Riemann surfaces and Weierstrass points and is a continuation of the authors' earlier work.
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ABSTRACT
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ABSTRACT In this paper we analyze the structure of transitive permutation groups that have trivial four point stabilizers, but some nontrivial three point stabilizer. In particular we give a complete, detailed classification when the... more
ABSTRACT In this paper we analyze the structure of transitive permutation groups that have trivial four point stabilizers, but some nontrivial three point stabilizer. In particular we give a complete, detailed classification when the group is simple or quasisimple. This paper is motivated by questions concerning the relationship between fixed points of automorphisms of Riemann surfaces and Weierstrass points and is a continuation of the authors' earlier work.
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G 2 (q), q = 3 2m+1 . Let T be an F -invariant maximal torus of G, and let B and B be F -invariant Borel subgroups intersecting in T with unipotent radicals U respectively U . By N we denote the normalizer NG (T ). Let be the root system... more
G 2 (q), q = 3 2m+1 . Let T be an F -invariant maximal torus of G, and let B and B be F -invariant Borel subgroups intersecting in T with unipotent radicals U respectively U . By N we denote the normalizer NG (T ). Let be the root system of G with respect to T and fa; bg its base given by B, where a is a short and b a long root. Now U respectively U is generated by subgroups X r respectively X r , where r 2 + (the set of positive roots). The g
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We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.
G 2 (q), q = 32m+1. Let T be an F -invariant maximal torus of G, andlet B and B be F -invariant Borel subgroups intersecting in T with unipotent radicals Urespectively U . By N we denote the normalizer NG (T ). Let be the root system of... more
G 2 (q), q = 32m+1. Let T be an F -invariant maximal torus of G, andlet B and B be F -invariant Borel subgroups intersecting in T with unipotent radicals Urespectively U . By N we denote the normalizer NG (T ). Let be the root system of Gwith respect to T and fa; bg its base given by
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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 restriction of the minimal representation... 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 restriction of the minimal representation of $E_7$ to the dual pair $G_2 \times{}$Sp(6) gives the non-endoscopic Langlands lift of irreducible representations of $G_2$ to
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ABSTRACT Motivated by a question on Riemann surfaces, we consider permutation groups that act nonregularly, such that every nontrivial element has at most two fixed points. We describe the permutation groups with these properties and give... more
ABSTRACT Motivated by a question on Riemann surfaces, we consider permutation groups that act nonregularly, such that every nontrivial element has at most two fixed points. We describe the permutation groups with these properties and give a complete, detailed classification when the group is simple.
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Q > 4, \x( x )^X(^)\ ^ i if <? ^ 4, and \x( x )/x0-)\ ** 5/g if x is not a transvection in an odd characteristic symplectic group G. For fixed point ratios in groups of Lie type, sharper bounds were found by Liebeck and Saxl [16];... more
Q > 4, \x( x )^X(^)\ ^ i if <? ^ 4, and \x( x )/x0-)\ ** 5/g if x is not a transvection in an odd characteristic symplectic group G. For fixed point ratios in groups of Lie type, sharper bounds were found by Liebeck and Saxl [16]; one has/(:c, Q) =s 4/3q apart from a few easily-understood ...
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Let G be either a split SO(2n+2), or a split adjoint group of type En, (n=6,7,8), over a p-adic field. In this article we study correspondences arising by restricting the minimal representation of G to various dual pairs in G.
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Page 1. BASE SIZES AND REGULAR ORBITS FOR COPRIME AFFINE PERMUTATION GROUPS DAVID GLUCK KAY MAGAARD 0. Introduction Let G be a permutation group on a finite set Ω. A sequence Bl(ω " ,
,ω b ) of ...