Kazhdan--Lusztig polynomials arise in the context of Hecke algebras associated to Coxeter groups. The computation of these polynomials is very difficult for examples of even moderate rank. It known that the leading coefficients, \mu(x,w) all 0 or 1 when x is fully commutative in type A, but in type D there are certain "bad" elements that make \mu value computation difficult. I will investigate a projection of the Kazhdan--Lusztig basis of the Hecke algebra with the goal of computing \mu values involving these "bad" elements.
A Projection of the Kazhdan--Lusztig Basis in Type D II
A Projection of the Kazhdan--Lusztig Basis in Type D II