Displaying similar documents to “Harmonic maps and representations of non-uniform lattices of PU ( m , 1 ) ”

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,...

Constructing equivariant maps for representations

Stefano Francaviglia (2009)

Annales de l’institut Fourier

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We show that if Γ is a discrete subgroup of the group of the isometries of ℍ k , and if ρ is a representation of Γ into the group of the isometries of ℍ n , then any ρ -equivariant map F : ℍ k → ℍ n extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Then, we show that the weak extension we obtain is actually a measurable...

Effective equidistribution of S-integral points on symmetric varieties

Yves Benoist, Hee Oh (2012)

Annales de l’institut Fourier

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Let K be a global field of characteristic not 2. Let Z = H ∖ G be a symmetric variety defined over K and S a finite set of places of K . We obtain counting and equidistribution results for the S-integral points of Z . Our results are effective when K is a number field.

Relative property (T) and linear groups

Talia Fernós (2006)

Annales de l’institut Fourier

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Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group Γ admits a special linear representation with non-amenable R -Zariski closure if and only if it acts on an Abelian...

Quadratic Differentials and Equivariant Deformation Theory of Curves

Bernhard Köck, Aristides Kontogeorgis (2012)

Annales de l’institut Fourier

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Given a finite p -group G acting on a smooth projective curve X over an algebraically closed field k of characteristic p , the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of G acting on the space V of global holomorphic quadratic differentials on X . We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when G is cyclic or when the action of G on...