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See detailCompatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image
Arias De Reyna Dominguez, Sara UL; Dieulefait, Luis; Wiese, Gabor UL

in Pacific Journal of Mathematics (2016), 281(1), 1-16

This article is the second part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part is concerned with ... [more ▼]

This article is the second part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part is concerned with symplectic Galois representations having a huge residual image, by which we mean that a symplectic group of full dimension over the prime field is contained up to conjugation. We prove a classification result on those subgroups of a general symplectic group over a finite field that contain a nontrivial transvection. Translating this group theoretic result into the language of symplectic representations whose image contains a nontrivial transvection, these fall into three very simply describable classes: the reducible ones, the induced ones and those with huge image. Using the idea of an (n,p)-group of Khare, Larsen and Savin we give simple conditions under which a symplectic Galois representation with coefficients in a finite field has a huge image. Finally, we combine this classification result with the main result of the first part to obtain a strenghtened application to the inverse Galois problem. [less ▲]

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See detailEigenvalues and entropies under the harmonic-Ricci flow
Li, Yi UL

in Pacific Journal of Mathematics (2014), 267(1), 141-184

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See detailAN ANALOGUE OF KREIN’S THEOREM FOR SEMISIMPLE LIE GROUPS
Pusti, Sanjoy UL

in Pacific Journal of Mathematics (2011), 254(2), 381395

We give an integral representation of $K$-positive definite functions on a real rank $n$ connected, noncompact, semisimple Lie group with finite centre. Moreover, we characterize the $\lambda$'s for which ... [more ▼]

We give an integral representation of $K$-positive definite functions on a real rank $n$ connected, noncompact, semisimple Lie group with finite centre. Moreover, we characterize the $\lambda$'s for which the $\tau$-spherical function $\phi_{\sigma,\lambda}^\tau$ is positive definite for the group $G=\mathrm{Spin}_e(n,1)$ and the complex spin representation $\tau$. [less ▲]

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See detailInvariance of the BFV complex
Schatz, Florian UL

in Pacific Journal of Mathematics (2010), 248(2), 453-474

The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold S of a Poisson manifold (M, \Pi ... [more ▼]

The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold S of a Poisson manifold (M, \Pi). However the assignment (coisotropic submanifold) -> (differential graded Poisson algebra) is not canonical, since in the construction several choices have to be made. One has to fix: 1. an embedding of the normal bundle NS of S into M as a tubular neighbourhood, 2. a connection on NS and 3. a special element Omega. We show that different choices of a connection and an element Omega -- but with the tubular neighbourhood fixed -- lead to isomorphic differential graded Poisson algebras. If the tubular neighbourhood is changed too, invariance can be restored at the level of germs. [less ▲]

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See detailStrongly r-matrix induced tensors, Koszul cohomology and arbitrary-dimensional quadratic Poisson cohomology
Ammar, Mourad UL; Kass, Guy; Masmoudi, Mohsen et al

in Pacific Journal of Mathematics (2010), 245(1), 1--23

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See detailCharacterization of the simple L¹(G) -modules for exponential Lie groups
Ludwig, Jean; Mint Elhacen, Salma; Molitor-Braun, Carine UL

in Pacific Journal of Mathematics (2003), 212(1), 133-156

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