Papers by Carlos Florentino
Linear Algebra and its Applications, 2009
Let A = (A1, ..., An, ...) be a finite or infinite sequence of 2 × 2 matrices with entries in an ... more Let A = (A1, ..., An, ...) be a finite or infinite sequence of 2 × 2 matrices with entries in an integral domain. We show that, except for a very special case, A is (simultaneously) triangularizable if and only if all pairs (Aj, A k ) are triangularizable, for 1 ≤ j, k ≤ ∞. We also provide a simple numerical criterion for triangularization.
We obtain an explicit characterization of the stable points of the action of G=SL(2,C) on the car... more We obtain an explicit characterization of the stable points of the action of G=SL(2,C) on the cartesian product G^n by simultaneous conjugation on each factor, in terms of the corresponding invariant functions, and derive from it a simple criterion for irreducibility of representations of finitely generated groups into G. We also obtain analogous results for the action of SL(2,C) on the vector space of n-tuples of 2 by 2 complex matrices. For a free group F_n of rank n, we show how to generically reconstruct the 2^{n-2} conjugacy classes of representations F_n -> G from their values under the map T_n : G^n = Hom(F_n,G) -> C^{3n-3} considered in [M], defined by certain 3n-3 traces of words of length one and two.
Using constructive methods in invariant theory, we define a map (with the minimal number of invar... more Using constructive methods in invariant theory, we define a map (with the minimal number of invariants) that distinguishes simultaneous similarity classes for non-commutative sequences over a field of characteristic $\neq2$. We also describe canonical forms for sequences of $2\times2$ matrices over algebraically closed fields, and give a method for finding sequences with a given set of invariants.
We obtain an explicit characterization of the stable points of the action of G=SL(2,C) on the car... more We obtain an explicit characterization of the stable points of the action of G=SL(2,C) on the cartesian product G^n by simultaneous conjugation on each factor, in terms of the corresponding invariant functions, and derive from it a simple criterion for irreducibility of representations of finitely generated groups into G. We also obtain analogous results for the action of SL(2,C) on the vector space of n-tuples of 2 by 2 complex matrices. For a free group F_n of rank n, we show how to generically reconstruct the 2^{n-2} conjugacy classes of representations F_n -> G from their values under the map T_n : G^n = Hom(F_n,G) -> C^{3n-3} considered in [M], defined by certain 3n-3 traces of words of length one and two.
Manuscripta Mathematica, 2001
We study a natural map from representations of a free group of rank g in GL(n,ℂ), to holomorphic ... more We study a natural map from representations of a free group of rank g in GL(n,ℂ), to holomorphic vector bundles of degree 0 over a compact Riemann surface X of genus g, associated with a Schottky uniformization of X. Maximally unstable flat bundles are shown to arise in this way. We give a necessary and sufficient condition for this map to be a submersion, when restricted to representations producing stable bundles. Using a generalized version of Riemann's bilinear relations, this condition is shown to be true on the subspace of unitary Schottky representations.
Linear Algebra and Its Applications, 2009
Let A=(A1,…,An,…)A=(A1,…,An,…) be a finite or infinite sequence of 2×22×2 matrices with entries i... more Let A=(A1,…,An,…)A=(A1,…,An,…) be a finite or infinite sequence of 2×22×2 matrices with entries in an integral domain. We show that, except in a very special case, AA is (simultaneously) triangularizable if and only if all pairs (Aj,Ak)(Aj,Ak) are triangularizable, for 1⩽j,k⩽∞1⩽j,k⩽∞. We also provide a simple numerical criterion for triangularization.Using constructive methods in invariant theory, we define a map (with the minimal number of invariants) that distinguishes simultaneous similarity classes for non-commutative sequences over a field of characteristic ≠2≠2. We also describe canonical forms for sequences of 2×22×2 matrices over algebraically closed fields, and give a method for finding sequences with a given set of invariants.
Journal of Functional Analysis, 2005
It is shown that the heat operator in the Hall coherent state transform for a compact Lie group K... more It is shown that the heat operator in the Hall coherent state transform for a compact Lie group K (J. Funct. Anal. 122 (1994) 103–151) is related with a Hermitian connection associated to a natural one-parameter family of complex structures on T*KT*K. The unitary parallel transport of this connection establishes the equivalence of (geometric) quantizations of T*KT*K for different choices of complex structures within the given family. In particular, these results establish a link between coherent state transforms for Lie groups and results of Hitchin (Comm. Math. Phys. 131 (1990) 347–380) and Axelrod et al. (J. Differential Geom. 33 (1991) 787–902).
International Journal of Mathematics, 2014
We study a natural map from representations of a free (resp. free abelian) group of rank g in GLr... more We study a natural map from representations of a free (resp. free abelian) group of rank g in GLr(C), to holomorphic vector bundles of degree zero over a compact Riemann surface X of genus g (resp. complex torus X of dimension g). This map defines what is called a Schottky functor. Our main result is that this functor induces an equivalence between the category of unipotent representations of Schottky groups and the category of unipotent vector bundles on X. We also show that, over a complex torus, any vector or principal bundle with a flat holomorphic connection is Schottky.
Geometriae Dedicata, 2007
We obtain an explicit characterization of the stable points of the action of $${G=SL(2,\mathbb{C}... more We obtain an explicit characterization of the stable points of the action of $${G=SL(2,\mathbb{C})}$$ on the cartesian product G � n by simultaneous conjugation on each factor in terms of the corresponding invariant functions. From this, a simple criterion for the irreducibility of representations of finitely generated groups into G is derived. We also obtain analogous results for the action
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Papers by Carlos Florentino