Displaying similar documents to “Conformally invariant trilinear forms on the sphere”

Inverse spectral results on even dimensional tori

Carolyn S. Gordon, Pierre Guerini, Thomas Kappeler, David L. Webb (2008)

Annales de l’institut Fourier

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Given a Hermitian line bundle L over a flat torus M , a connection on L , and a function Q on M , one associates a Schrödinger operator acting on sections of L ; its spectrum is denoted S p e c ( Q ; L , ) . Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections , and we address the extent to which the spectrum S p e c ( Q ; L , ) determines the potential Q . With a genericity condition, we show that if the connection is invariant...

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,...

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.

Geometric Invariant Theory and Generalized Eigenvalue Problem II

Nicolas Ressayre (2011)

Annales de l’institut Fourier

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Let G be a connected reductive subgroup of a complex connected reductive group G ^ . Fix maximal tori and Borel subgroups of G and G ^ . Consider the cone ( G , G ^ ) generated by the pairs ( ν , ν ^ ) of strictly dominant characters such that V ν * is a submodule of V ν ^ . We obtain a bijective parametrization of the faces of ( G , G ^ ) as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.

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...