Reflection Groups and Coxeter Groups
By Alexandre V. Borovik, Gel'fand Im, N. White. 2003
482 citations recorded by the source corpus.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/d6efc0407da8d2fe190f1cf2bfce0bf039ccfd7f
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In Discrete Mathematics and Combinatorics
- Geordie Williamson
- Ben Elias
- Takuro Abe
- Hiroaki Terao
- Khalifa Trimeche
- Thomas Lam
- Mark Shimozono
- Jennifer Morse
In Geometry and Topology
- Ben Elias
- Geordie Williamson
- Takuro Abe
- Khalifa Trimeche
- Michael Cuntz
- Thomas Lam
- L. T. Jensen
- David E. Speyer
In Materials Chemistry
Citations in the corpus
- The freeness of ideal subarrangements of Weyl arrangements (2013, background): “Our standard references on root systems are [3] and [5].”
- Sortable elements and Cambrian lattices (2005, unknown): “(More detail, including proofs of assertions not proven here, can be found in one of the standard references [4, 5, 13].)”
- Affine Stanley symmetric functions (2005, methodology): “By general facts concerning parabolic subgroups of Coxeter groups [10], the minimal length coset representative ¯w of a coset S n ♦ ) w is unique and satisfies l ( u¯w ) = l ( u ) + l ( ¯w ) for any u ∈ S n ♦ .”
- Constructing Weyl group multiple Dirichlet series (2008, unknown): “For more details we refer to [Hum90].”
- On parabolic subgroups of Artin groups (2022, unknown): “For more information on the length function of Coxeter groups see [Hum90].”
- The volume product of convex bodies with many hyperplane symmetries (2013, unknown): “This theorem will be deduced from our previous results using the following structural statement, which relies on Coxeter’s classification of finite reflection groups [3] (see also [4, 9]).”
- Cambrian Lattices (2004, unknown): “We assume basic definitions and results on root systems, for which the reader is referred to [6, 18].”
- Sheaves on affine Schubert varieties, modular representations and Lusztig's conjecture (2007, unknown): “It has all the properties listed in Section 4.1 (for property (3), see [Hum90, Proposition 5.9]).”
- Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators (2002, methodology): “In this section we collect some notations and results on Dunkl operators and the Dunkl kernel (see [4, 5, 8, 11, 12]).”
- The Hodge theory of Soergel bimodules (2012, background): “The following positivity property of the representation h plays an important role below (see [Bou81, V.4.3] or [Hum90, Lemma 5.13] and the proof of [Soe07, Prop.”