2,322 research outputs found
Reflections in abstract Coxeter groups
Let be a Coxeter group and a reflection. If the group of order 2
generated by is the intersection of all the maximal finite subgroups of
that contain it, then any isomorphism from to a Coxeter group must
take to a reflection in . The aim of this paper is to show how to
determine, by inspection of the Coxeter graph, the intersection of the maximal
finite sugroups containing . In particular we show that the condition above
is satisfied whenever is infinite and irreducible, and has the property
that all rank two parabolic subgroups are finite. So in this case all
isomorphisms map reflections to reflections.Comment: 25 pages, 0 figure
W-graph ideals
We introduce a concept of a W-graph ideal in a Coxeter group. The main goal
of this paper is to describe how to construct a W-graph from a given W-graph
ideal. The principal application of this idea is in type A, where it provides
an algorithm for the construction of W-graphs for Specht modules.Comment: 25 page
VSCE technology definition study
Refined design definition of the variable stream control engine (VSCE) concept for advanced supersonic transports is presented. Operating and performance features of the VSCE are discussed, including the engine components, thrust specific fuel consumption, weight, noise, and emission system. A preliminary engine design is presented
On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups
In this paper we prove, without the finite rank assumption, that any
irreducible Coxeter group of infinite order is directly indecomposable as an
abstract group. The key ingredient of the proof is that we can determine, for
an irreducible Coxeter group, the centralizers of the normal subgroups that are
generated by involutions. As a consequence, we show that the problem of
deciding whether two general Coxeter groups are isomorphic, as abstract groups,
is reduced to the case of irreducible Coxeter groups, without assuming the
finiteness of the number of the irreducible components or their ranks. We also
give a description of the automorphism group of a general Coxeter group in
terms of those of its irreducible components.Comment: 30 page
Putative multiple alleles at the vegetative (heterokaryon) incompatibility loci het-c and het-8 in Neurospora crassa
It has never been determined in Neurospora whether multiple alleles exist at individual het loci such that interaction between any two unlike alleles will result in an incompatibility reaction. The evidence summarized here from recombination genetics and from sampling natural populations suggests multiple allelism at two of the best studied het loci. However, an alternate explanation is not excluded that invokes linked multiple loci rather than multiple alleles
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