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[more ▼]Consider a three dimensional cusped spherical CR manifold M and suppose that the holonomy representation of $\pi_1(M)$ can be deformed in such a way that the peripheral holonomy is generated by a non-parabolic element. We prove that, in this case, there is a spherical CR structure on some Dehn surgeries of M. The result is very similar to R. Schwartz's spherical CR Dehn surgery theorem, but has weaker hypotheses and does not give the uniformizability of the structure. We apply our theorem in the case of the Deraux-Falbel structure on the Figure Eight knot complement and obtain spherical CR structures on all Dehn surgeries of slope $-3 + r$ for $r \in \mathbb{Q}^{+}$ small enough. [less ▲]Detailed reference viewed: 49 (1 UL) Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge imageArias De Reyna Dominguez, Sara ; Dieulefait, Luis; Wiese, Gabor in Pacific Journal of Mathematics (2016), 281(1), 1-16This 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 ▲]Detailed reference viewed: 103 (4 UL) Eigenvalues and entropies under the harmonic-Ricci flowLi, Yi in Pacific Journal of Mathematics (2014), 267(1), 141-184Detailed reference viewed: 67 (4 UL) AN ANALOGUE OF KREIN’S THEOREM FOR SEMISIMPLE LIE GROUPSPusti, Sanjoy in Pacific Journal of Mathematics (2011), 254(2), 381395We 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 ▲]Detailed reference viewed: 64 (2 UL) Strongly r-matrix induced tensors, Koszul cohomology and arbitrary-dimensional quadratic Poisson cohomologyAmmar, Mourad ; Kass, Guy; Masmoudi, Mohsen et alin Pacific Journal of Mathematics (2010), 245(1), 1--23Detailed reference viewed: 116 (4 UL) Invariance of the BFV complexSchatz, Florian in Pacific Journal of Mathematics (2010), 248(2), 453-474The 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 ▲]Detailed reference viewed: 25 (0 UL) Characterization of the simple L¹(G) -modules for exponential Lie groupsLudwig, Jean; Mint Elhacen, Salma; Molitor-Braun, Carine in Pacific Journal of Mathematics (2003), 212(1), 133-156Detailed reference viewed: 74 (1 UL) 1