Interdisciplinary Seminar Series

Title: A new Analog of Permutation Patterns for General Coxeter groups

Speaker: Matthew Samuel, Rutgers University

Date: Monday, February 4, 2013 11:00am - 12:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ


We discuss our recent generalization of the concept of a permutation pattern to general Coxeter groups and relate it to the usual definition as well as other generalizations. We prove a conjecture of Billey and Crites characterizing the smooth Schubert varieties in affine type A and prove that smoothness of Schubert varieties in any Kac-Moody group is a pattern avoidance property in our sense. We show that an element of a Coxeter group has at least as many commutation classes of reduced words as any closed pattern it contains. We then relate our patterns to Kazhdan-Lusztig polynomials and discuss our ideas toward proving some longstanding conjectures.

DIMACS/CCICADA Interdisciplinary Series, Complete Calendar