53 research outputs found
Recommended from our members
On reflection subgroups of finite Coxeter groups
Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy
Recommended from our members
Coxeter arrangements and Solomon's descent algebra
In our recent paper [3], we claimed that both the group algebra of a finite Coxeter group W as well as the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional representations of centralizers, one for each conjugacy class of elements of W, and gave a uniform proof of this claim for symmetric groups. In this note we outline an inductive approach to our conjecture. As an application of this method, we prove the inductive version of the conjecture for nite Coxeter groups of rank up to 2
Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six
In recent papers we have refined a conjecture of Lehrer and Solomon
expressing the character of a finite Coxeter group acting on the th
graded component of its Orlik-Solomon algebra as a sum of characters induced
from linear characters of centralizers of elements of . Our refined
conjecture relates the character above to a component of a decomposition of the
regular character of related to Solomon's descent algebra of . The
refined conjecture has been proved for symmetric and dihedral groups, as well
as finite Coxeter groups of rank three and four.
In this paper, the second in a series of three dealing with groups of rank up
to eight (and in particular, all exceptional Coxeter groups), we prove the
conjecture for finite Coxeter groups of rank five and six, further developing
the algorithmic tools described in the previous article. The techniques
developed and implemented in this paper provide previously unknown
decompositions of the regular and Orlik-Solomon characters of the groups
considered.Comment: Final Version. 17 page
On Reflection Subgroups of Finite Coxeter Groups
Let be a finite Coxeter group. We classify the reflection subgroups of
up to conjugacy and give necessary and sufficient conditions for the map
that assigns to a reflection subgroup of the conjugacy class of its
Coxeter elements to be injective, up to conjugacy.Comment: 17 pages; final version, to appear in Comm. Algebr
Нанесение антифрикционных покрытий порошком Б-83 методом холодного газодинамического напыления
Работа направлена на развитие технологии холодного газодинамического напыления антифрикционного покрытия порошком Б-83 на подшипники скольжения судовые. Как альтернатива традиционному методу баббитозаливки судовых подшипников скольжения.The work is aimed at the development of technology of cold gas-dynamic spraying of antifriction coating with powder B-83 on ship bearings. As an alternative to the traditional method of babiogorski marine bearings
Cohomology of Coxeter arrangements and Solomon's descent algebra
We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group W and relate it to the descent algebra of W. As a result, we claim that both the group algebra of W and the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional representations of element centralizers, one for each conjugacy class of elements of W. We give a uniform proof of the claim for symmetric groups. In addition, we prove that a relative version of the conjecture holds for every pair (W, W-L), where W is arbitrary and W-L is a parabolic subgroup of W, all of whose irreducible factors are of type A.The authors would like to acknowledge support from the DFG-priority programme
SPP1489 “Algorithmic and Experimental Methods in Algebra, Geometry,
and Number Theory”. Part of the research for this paper was carried out
while the authors were staying at the Mathematical Research Institute Oberwolfach
supported by the “Research in Pairs” programme. The second author wishes
to acknowledge support from Science Foundation Ireland.peer-reviewe
- …