Generalized Bott-Samelson resolutions for Schubert varieties
This talk focuses on generalized Bott-Samelson resolutions of Schubert varieties. These resolutions are iterated G/P-bundles (for different parabolic subgroups P of the algebraic group G). Special cases have appeared in the work of Zelevinsky, Wolper, Ryan and several other authors. After introducing these resolutions and some of their properties, we discuss a possible best resolution for a given Schubert variety X(w), based on a combinatorial condition on the inversion set of the Weyl group element w. If time permits, we will discuss a computer program that calculates local intersection cohomology (i.e., Kazhdan-Lusztig polynomials) from these resolutions. This is joint work with Jennifer Koonz.