Displaying similar documents to “Constructing equivariant maps for representations”

Embedding theorems for Müntz spaces

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2011)

Annales de l’institut Fourier

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We discuss boundedness and compactness properties of the embedding M Λ 1 ⊂ L 1 ( μ ) , where M Λ 1 is the closed linear span of the monomials x λ n in L 1 ( [ 0 , 1 ] ) and μ is a finite positive Borel measure on the interval [ 0 , 1 ] . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences Λ . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators...

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let A , B denote generic binary forms, and let 𝔲 r = ( A , B ) r denote their r -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the { 𝔲 r } . As a consequence, we show that each of the higher transvectants { 𝔲 r : r ≥ 2 } is redundant in the sense that it can be completely recovered from 𝔲 0 and 𝔲 1 . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of S L 2 -representations,...

Harmonic maps and representations of non-uniform lattices of PU ( m , 1 )

Vincent Koziarz, Julien Maubon (2008)

Annales de l’institut Fourier

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We study representations of lattices of PU ( m , 1 ) into PU ( n , 1 ) . We show that if a representation is reductive and if m is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic m -space to complex hyperbolic n -space. This allows us to give a differential geometric proof of rigidity results obtained by M. Burger and A. Iozzi. We also define a new invariant associated to representations into PU ( n , 1 ) of non-uniform lattices in PU ( 1 , 1 ) , and more generally of fundamental groups...

Geometry of currents, intersection theory and dynamics of horizontal-like maps

Tien-Cuong Dinh, Nessim Sibony (2006)

Annales de l’institut Fourier

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We introduce a geometry on the cone of positive closed currents of bidegree ( p , p ) and apply it to define the intersection of such currents. We also construct and study the Green currents and the equilibrium measure for horizontal-like mappings. The Green currents satisfy some extremality properties. The equilibrium measure is invariant, mixing and has maximal entropy. It is equal to the intersection of the Green currents associated to the horizontal-like map and to its inverse.