A symmetric group action on the irreducible components of the Shi variety associated to \(W({\widetilde{a}}_n)\)

DOI10.1007/s10801-023-01243-5zbMath1526.20054arXiv2010.05602OpenAlexW3091770684MaRDI QIDQ6083968

Nathan Chapelier-Laget

Publication date: 31 October 2023

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.05602

zbMATH Keywords

latticeaffine Weyl groupcrystallographic root systemmaximal reflection subgroup

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Other geometric groups, including crystallographic groups (20H15) Root systems (17B22)

Cites Work

• Small roots, low elements, and the weak order in Coxeter groups
• An order on circular permutations
• Lattice associated to a Shi variety
• Combinatorics of Coxeter Groups
• Alcoves Corresponding to an Affine Weyl Group
• Reflection groups and invariant theory
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