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Metaplectic covers of G L n and the Gauss-Schering lemma

Richard Hill (2001)

Journal de théorie des nombres de Bordeaux

The Gauss-Schering Lemma is a classical formula for the Legendre symbol commonly used in elementary proofs of the quadratic reciprocity law. In this paper we show how the Gauss Schering Lemma may be generalized to give a formula for a 2 -cocycle corresponding to a higher metaplectic extension of GL n / k for any global field k . In the case that k has positive characteristic, our formula gives a complete construction of the metaplectic group and consequently an independent proof of the power reciprocity...

Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs

Mikhail Ostrovskii (2014)

Analysis and Geometry in Metric Spaces

We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups.We compare characterizations of superrefiexivity in terms of diamond graphs and binary trees.We show that there exist sequences of series-parallel graphs of increasing topological complexitywhich admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superrefiexivity.

Metric Ricci Curvature and Flow for PL Manifolds

Emil Saucan (2013)

Actes des rencontres du CIRM

We summarize here the main ideas and results of our papers [28], [14], as presented at the 2013 CIRM Meeting on Discrete curvature and we augment these by bringing up an application of one of our main results, namely to solving a problem regarding cube complexes.

Minimal formations of universal algebras

Wenbin Guo, K.P. Shum (2001)

Discussiones Mathematicae - General Algebra and Applications

A class ℱ of universal algebras is called a formation if the following conditions are satisfied: 1) Any homomorphic image of A ∈ ℱ is in ℱ; 2) If α₁, α₂ are congruences on A and A / α i ∈ ℱ , i = 1,2, then A/(α₁∩α₂) ∈ ℱ. We prove that any formation generated by a simple algebra with permutable congruences is minimal, and hence any formation containing a simple algebra, with permutable congruences, contains a minimum subformation. This result gives a partial answer to an open problem of Shemetkov and Skiba...

Minimal length coset representatives for quotients of parabolic subgroups in Coxeter groups

Fabio Stumbo (2000)

Bollettino dell'Unione Matematica Italiana

In questo lavoro viene trovata un'espressione esplicita per i rappresentanti dei laterali di sottogrupi parabolici di gruppi di Coxeter aventi lunghezza minima: dato un sistema di Coxeter W , S ed un suo sottogruppo parabolico W I , I , con I ⊂ S , si determina esplicitamente in ogni laterale W I ⁢ w di W I un elemento avente lunghezza minima. Nella sezione 2 trattiamo i casi classici, i.e. W = A n , B n e D n . Dopo ciò, nella sezione 3, diamo una procedura per risolvere il problema nei restanti casi eccezionali, insieme a qualche...

Currently displaying 81 – 100 of 246