Metric groups, unitary representations and continuous logic

Aleksander Ivanov

Displaying similar documents to “Metric groups, unitary representations and continuous logic”

Amenability and Ramsey theory in the metric setting

Adriane Kaïchouh (2015)

Fundamenta Mathematicae

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Moore [Fund. Math. 220 (2013)] characterizes the amenability of the automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to the automorphism groups of metric Fraïssé structures, which encompass all Polish groups. As an application, we prove that amenability is a $G_{δ}$ condition.

On the representation theory of braid groups

Ivan Marin (2013)

Annales mathématiques Blaise Pascal

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This work presents an approach towards the representation theory of the braid groups $B_{n}$ . We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids, with the help of Drinfeld associators. We set a dictionary between representation-theoretic properties of these two structures, and tools to describe the representations thus obtained. We give an explanation for the frequent apparition of unitary structures...

Decomposition numbers modulo p of certain representations of the groups $S L_{n} (p^{k}), S U_{n} (p^{k}), S p_{2 n} (p^{k})$

A. Zalesskii (1990)

Banach Center Publications

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For Coxeter groups $z^{| g |}$ is a coefficient of a uniformly bounded representation

Tadeusz Januszkiewicz (2002)

Fundamenta Mathematicae

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We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.

Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi (2014)

Annales de l’institut Fourier

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In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type $☆$ ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type $☆$ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...

Some remarks on Lorenzen $r$ -group of partly ordered groups

Jiří Močkoř, Angeliki Kontolatou (1996)

Czechoslovak Mathematical Journal

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Covering locally compact groups by less than $2^{ω}$ many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

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Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if $C_{E K}$ is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of $C_{E K}$ . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result...

Plane and layer $(p 2, 2^{l})$ symmetry groups

S. V. Jablan (1990)

Matematički Vesnik

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A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Robert Guralnick, Pham Tiep (2012)

Journal of the European Mathematical Society

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The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age $\leq 1$ . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation....

Plane and layer $(p^{p r i m e}, 2^{l})$ symmetry groups

S. V. Jablan (1990)

Matematički Vesnik

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Compact Abelian groups and extensions of Haar measures

A. Hulanicki

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ContentsIntroduction.................................................................................................................... 31. Preliminaries (topology measure).................................................................... 32. Problems and the theorem.................................................................................... 73. Preliminaries (abstract groups, Cartesian products)....................................... 94. Preliminaries (automorphisms, duality...

A descriptive view of unitary group representations

Simon Thomas (2015)

Journal of the European Mathematical Society

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In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if $G$ and $H$ are countable amenable non-type I groups, then the unitary duals of $G$ and $H$ are Borel isomorphic.