The University of Michigan Combinatorics Seminar
Fall 2001
October 5, 4:10-5:00, 3866 East Hall





A Root System Description of Pattern Avoidance with Applications to G/B

Sara Billey

MIT




Abstract

Pattern avoidance has been used to classify several notions for permutations and signed permutations. In this talk, we propose a new generalization of pattern avoidance which can be applied to all root systems and their Weyl groups. The main theorem shows that for any semisimple Lie group G and maximal Borel subgroup B, smooth Schubert varieties in G/B can be characterized by this new method with a very short list of patterns.

This is joint work with A. Postnikov.