Standard objects in 2-braid groups
Nicolas Libedinsky, Geordie Williamson
TL;DR
This paper proves the existence of standard and costandard objects in 2-braid groups for any Coxeter system, extending known results in category O and confirming a conjecture by Rouquier.
Contribution
It establishes the existence of these objects in a general setting, broadening the understanding of 2-braid groups and their categorical structures.
Findings
Existence of standard and costandard objects in 2-braid groups for all Coxeter systems.
Generalization of the extension vanishing formula in category O.
Confirmation of Rouquier's conjecture.
Abstract
For any Coxeter system we establish the existence (conjectured by Rouquier) of analogues of standard and costandard objects in 2-braid groups. This generalizes a known extension vanishing formula in the BGG category O.
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