Canonical bases of invariant polynomials for the irreducible reflection groups of types E6, E7, and E8
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DOI: 10.1016/j.jalgebra.2018.01.017
Abstract: Abstract Given a rank n irreducible finite reflection group W, the W-invariant polynomial functions defined in R n can be written as polynomials of n algebraically independent homogeneous polynomial functions, p 1 ( x )… read more here.
Keywords: canonical bases; groups types; bases invariant; invariant polynomials ... See more keywords
Perfect isometries between blocks of complex reflection groups
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DOI: 10.1016/j.jalgebra.2019.04.031
Abstract: Acknowledgements.The authors are grateful to M. Broue for asking the question this article settles, at the end of a talk given by the first author at the Beijing Center for Mathematical Research during the Third… read more here.
Keywords: blocks complex; complex reflection; research; isometries blocks ... See more keywords
Circle packings, kissing reflection groups and critically fixed anti-rational maps
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DOI: 10.1017/fms.2021.81
Abstract: Abstract In this article, we establish an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps. The correspondence, which is expressed using simple planar graphs, has several dynamical consequences. As an application of… read more here.
Keywords: rational maps; fixed anti; reflection groups; kissing reflection ... See more keywords
Three-dimensional representations of braid groups associated with some finite complex reflection groups
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DOI: 10.1142/s0129167x17501099
Abstract: We study the rigidity of three-dimensional representations of braid groups associated with finite primitive irreducible complex reflection groups in GL(3, ℂ). In many cases, we show the rigidity. For rigid representations, we give explicit forms… read more here.
Keywords: three dimensional; complex reflection; representations braid; dimensional representations ... See more keywords
Hospital ethics reflection groups: a learning and development resource for clinical practice
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DOI: 10.1186/s12910-019-0415-5
Abstract: BackgroundAn ethics reflection group (ERG) is one of a number of ethics support services developed to better handle ethical challenges in healthcare. The aim of this article is to evaluate the significance of ERGs in… read more here.
Keywords: clinical practice; hospital; significance; ethics reflection ... See more keywords
A McKay correspondence for reflection groups
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DOI: 10.1215/00127094-2019-0069
Abstract: We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies… read more here.
Keywords: correspondence reflection; correspondence; reflection groups; reflection ... See more keywords