Harmonic analysis on algebraic groups over two-dimensional local fields of equal characteristic

Author(s):  
Mikhail Kapranov
2017 ◽  
Vol 39 (3) ◽  
pp. 658-688 ◽  
Author(s):  
POLONA DURCIK ◽  
VJEKOSLAV KOVAČ ◽  
KRISTINA ANA ŠKREB ◽  
CHRISTOPH THIELE

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.


2014 ◽  
Vol 2 ◽  
Author(s):  
SYLVAIN BARRÉ ◽  
MIKAËL PICHOT

AbstractWe consider models of random groups in which the typical group is of intermediate rank (in particular, it is not hyperbolic). These models are parallel to Gromov’s well-known constructions, and include for example a ‘density model’ for groups of intermediate rank. The main novelty is the higher rank nature of the random groups. They are randomizations of certain families of lattices in algebraic groups (of rank 2) over local fields.


2018 ◽  
Vol 19 (4) ◽  
pp. 1031-1091
Author(s):  
Thierry Stulemeijer

Given a locally finite leafless tree $T$, various algebraic groups over local fields might appear as closed subgroups of $\operatorname{Aut}(T)$. We show that the set of closed cocompact subgroups of $\operatorname{Aut}(T)$ that are isomorphic to a quasi-split simple algebraic group is a closed subset of the Chabauty space of $\operatorname{Aut}(T)$. This is done via a study of the integral Bruhat–Tits model of $\operatorname{SL}_{2}$ and $\operatorname{SU}_{3}^{L/K}$, that we carry on over arbitrary local fields, without any restriction on the (residue) characteristic. In particular, we show that in residue characteristic $2$, the Tits index of simple algebraic subgroups of $\operatorname{Aut}(T)$ is not always preserved under Chabauty limits.


2014 ◽  
Vol 58 (1) ◽  
pp. 149-168 ◽  
Author(s):  
Ulrich Derenthal ◽  
Daniel Loughran

AbstractWe classify generically transitive actions of semi-direct products on ℙ2. Motivated by the program to study the distribution of rational points on del Pezzo surfaces (Manin's conjecture), we determine all (possibly singular) del Pezzo surfaces that are equivariant compactifications of homogeneous spaces for semi-direct products .


2004 ◽  
Vol 276 (1) ◽  
pp. 292-339 ◽  
Author(s):  
Mikhail Borovoi ◽  
Boris Kunyavskiı̆ ◽  
Philippe Gille

2011 ◽  
Vol 75 (4) ◽  
pp. 749-814 ◽  
Author(s):  
Denis V Osipov ◽  
Aleksei N Parshin

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Nathan Benjamin ◽  
Scott Collier ◽  
A. Liam Fitzpatrick ◽  
Alexander Maloney ◽  
Eric Perlmutter

Abstract We apply the theory of harmonic analysis on the fundamental domain of SL(2, ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2, ℤ), and of target space moduli space O(c, c; ℤ)\O(c, c; ℝ)/O(c)×O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.


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