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Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

Let H GL ( V ) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v V and let G = { g GL ( V ) g H v = H v } . Following Raïs we say that the orbit H v is characteristic for H if the identity component of G is H . If H is semisimple, we say that H v is semi-characteristic for H if the identity component of G is an extension of H by a torus. We classify the H -orbits which are not (semi)-characteristic in many cases.

Linear operators preserving maximal column ranks of nonbinary boolean matrices

Seok-Zun Song, Sung-Dae Yang, Sung-Min Hong, Young-Bae Jun, Seon-Jeong Kim (2000)

Discussiones Mathematicae - General Algebra and Applications

The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.

Local coordinates for SL ( n , C ) -character varieties of finite-volume hyperbolic 3-manifolds

Pere Menal-Ferrer, Joan Porti (2012)

Annales mathématiques Blaise Pascal

Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL ( 2 , C ) with the n -dimensional irreducible representation of SL ( 2 , C ) in SL ( n , C ) . In this paper we give local coordinates of the SL ( n , C ) -character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.

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