Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Algebra
Kazhdan-Lusztig Cells In Planar Hyperbolic Coxeter Groups And Automata, Mikhail V. Belolipetsky, Paul E. Gunnells, Richard A. Scott
Kazhdan-Lusztig Cells In Planar Hyperbolic Coxeter Groups And Automata, Mikhail V. Belolipetsky, Paul E. Gunnells, Richard A. Scott
Paul Gunnells
Let C be a one- or two-sided Kazhdan–Lusztig cell in a Coxeter group (W, S), and let Red(C) be the set of reduced expressions of all w ∈ C, regarded as a language over the alphabet S. Casselman has conjectured that Red(C) is regular. In this paper, we give a conjectural description of the cells when W is the group corresponding to a hyperbolic polygon, and show that our conjectures imply Casselman's.
Generalised Burnside Rings, G-Categories And Module Categories, Paul E. Gunnells, Andrew Rose, Dmitriy Rumynin
Generalised Burnside Rings, G-Categories And Module Categories, Paul E. Gunnells, Andrew Rose, Dmitriy Rumynin
Paul Gunnells
This note describes an application of the theory of generalised Burnside rings to algebraic representation theory. Tables of marks are given explicitly for the groups S4 and S5 which are of particular interest in the context of reductive algebraic groups. As an application, the base sets for the nilpotent element F4(a3) are computed.