Room 326

Subword Complexes in Coxeter Groups

K N Raghavan

IMSc

Fix a Coxeter group (e.g., the symmetric group with its natural set of
generators, the simple transpositions).     Given a word in the generators
and an element of the group,   there is associated to this pair a finite
simplicial complex,  called the subword complex.      We will observe that
such complexes are "vertex decomposable" and therefore "shellable".     This
will have algebraic and geometric consequences for matrix Schubert varieties
and therefore also for Schubert polynomials.    

Although,  thankfully, the talk is not logically dependent upon earlier
talks in the same seminar on the work of Knutson-Miller,  it does tie up
with the results discussed therein.