#### 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.

Done