Sum-product for real Lie groups

Abstract

We prove a discretized sum-product theorem for representations of Lie groups whose Jordan-Hölder decomposition does not contain the trivial representation. This expansion result is used to derive a product theorem in perfect Lie groups.

arXiv commentTo appear in Journal of the European Mathematical Society

References in corpus (5)

• Some connections between Falconer's distance set conjecture, and sets of Furstenburg type
• Measure expanding actions, expanders and warped cones
• Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups
• Borelian subgroups of simple Lie groups
• Super-approximation, II: the p-adic and bounded power of square-free integers cases

Cited by in corpus (5)

• Fourier transform of self-affine measures
• Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups
• On the dimension of exceptional parameters for nonlinear projections, and the discretized Elekes-Rónyai theorem
• Discretized Sum-product and Fourier decay in ${\mathbb{R}}^n$
• Dimension-expanding polynomials and the discretized Elekes-Rónyai theorem