Reflection Groups and Coxeter Groups

Humphreys, J. E. (1990). Reflection Groups and Coxeter Groups. Cambridge University Press.

Type

Book

Intellectual base

Review or monograph

Year

1990

DOI

10.1017/cbo9780511623646

ISBN

9780521375108

Link

https://doi.org/10.1017/cbo9780511623646

Cited by

3 citations across 3 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Coxeter Element
  • Humphreys treats Coxeter elements, eigenvalues, finite reflection groups, and the Coxeter number as an organizing part of the theory.
• Coxeter Notation
  • For geometric reflection realizations, an edge order (m_{ij}) corresponds to mirrors meeting at angle \(\pi/m_{ij}\) in the standard chamber description

    This sourceHumphreys classifies the finite reflection groups by numerically labelled Coxeter graph, including the noncrystallographic H3, H4 and I2(m), isolates the crystallographic condition where the Weyl/Dynkin apparatus applies, and carries the same graphs over to the affine and general infinite Coxeter groups.

• Root System
  • Bourbaki gives the systematic reflection, base, and classification theory. Humphreys develops the parallel Coxeter-group structure generated by the root reflections.

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Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://sites.math.washington.edu/~billey/classes/reflection.groups/references/Humphreys.ReflectionGroupsAndCoxeterGroups.pdf ×1

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