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Shi arrangements and low elements in Coxeter groups

open access: yesProceedings of the London Mathematical Society
AbstractGiven an arbitrary Coxeter system and a non‐negative integer , the ‐Shi arrangement of is a subarrangement of the Coxeter hyperplane arrangement of . The classical Shi arrangement () was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for .
Dyer, Matthew   +3 more
openaire   +2 more sources

Automorphic Bloch theorems for hyperbolic lattices. [PDF]

open access: yesProc Natl Acad Sci U S A, 2022
Maciejko J, Rayan S.
europepmc   +1 more source

Non-cancellable elements in type affine $C$ Coxeter groups

open access: yes, 2009
Let $(W,S)$ be a Coxeter system and suppose that $w \in W$ is fully commutative (in the sense of Stembridge) and has a reduced expression beginning (respectively, ending) with $s \in S$. If there exists $t\in S$ such that $s$ and $t$ do not commute and $tw$ (respectively, $wt$) is no longer fully commutative, we say that $w$ is left (respectively ...
openaire   +3 more sources

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