Algebra Seminar: Dyer -- Bruhat order, weak order and closure operators on root systems

Matthew Dyer (University of Notre Dame) 

Friday 28 April, 12-1pm, Place: Carslaw 375 

Title: Bruhat order, weak order and closure operators on root systems 

Abstract: Reflection orders of Coxeter groups are certain total orders of the
reflections (or positive roots).  They are analogues for infinite Coxeter groups of
reduced expressions of longest elements of finite Coxeter groups.  Their initial
sections parameterise (actually or conjecturally, depending on context) natural twists
of certain algebraic, geometric, combinatorial and representation theoretic objects
attached to Coxeter groups, such as Bruhat order.  Many long standing conjectures
concerning initial sections may be viewed as natural extensions, to a completion by
"infinitely long elements", of trivial or well known properties of weak order of
Coxeter groups.  This talk will survey recent results, some due to Francois Viard and
Weijia Wang, arising from attempts to refine, test and prove (at least in tractable
special cases) these conjectures.