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Improving an algorithm to solve multiple simultaneous conjugacy problems in braid groups
(American Mathematical Society, 2005)
There are recent cryptographic protocols that are based on Multiple Simultaneous Conjugacy Problems in braid groups. We improve an algorithm, due to Sang Jin Lee and Eonkyung Lee, to solve these problems, by applying a ...
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On simultaneous arithmetic progressions on elliptic curves
(Taylor & Francis, 2006)
In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples ...
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The defining ideals of conjugacy classes of nilpotent matrices and a conjecture of Weyman
(Oxford University Press, 2008)
Tanisaki introduced generating sets for the defining ideals of the schematic intersections of the closure of conjugacy classes of nilpotent matrices with the set of diagonal matrices. These ideals are naturally labeled by ...
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Continuous division of differential operators
(Association des Annales de l'Institut Fourier, 2001)
In this paper, we give a new proof of the continuity of division by differential operators with analytic coefficients, originally proved by Mebkhout and the second author. Our methods come from the proof of the Constant ...
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Combinatorics on a family of reduced Kronecker coefficients
(Académie des Sciences, 2015-08-28)
The reduced Kronecker coefficients are particular instances of Kronecker coefficients, that nevertheless contain enough information to compute all Kronecker coefficients from them. In this note, we compute the generating ...
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Logarithmic differential operators and logarithmic de Rham complexes relative to a free divisor
(Elsevier, 1999)
We prove a structure theorem for differential operators in the 0-th term of the V-filtration relative to a free divisor. manifold. As an application, we give a formula for the logarithmic de Rham complex with respect to a ...
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Irregular modified A-Hypergeometric systems
(American Mathematical Society, 2015)
A modified A-hypergeometric system is a system of differential equations for the function f(t w · x) where f(y) is a solution of an A-hypergeometric system in n variables and w is an n dimensional integer vector, which is ...
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Computation of centralizers in braid groups and Garside groups
(Consejo Superior de Investigaciones Científicas, 2003)
We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in [9] ...
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Tame Galois realizations of GSp4 (Fℓ) over Q
(Oxford University Press, 2011)
In this paper we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic ℓ > 3 as the Galois group of a tamely ramified Galois extension of Q. The strategy is to consider ...
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Partial symmetries of iterated plethysms
(Springer, 2023-05-03)
This work highlights the existence of partial symmetries in large families of iterated plethystic coefficients. The plethystic coefficients involved come from the expansion in the Schur basis of iterated plethysms of Schur ...