Date of Award
Doctor of Philosophy (PhD)
Richard M. Green
James M. Douglass
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. In type A it is known that the leading coefficient, μ(x, w) of a Kazhdan–Lusztig polynomial Px,w is either 0 or 1 when x is fully commutative and w is arbitrary. In type D Coxeter groups there are certain "bad" elements that make μ-value computation difficult. The Robinson–Schensted correspondence between the symmetric group and pairs of standard Young tableaux gives rise to a way to compute cells of Coxeter groups of type A. A lesser known correspondence exists for signed permutations and pairs of so-called domino tableaux, which allows us to compute cells in Coxeter groups of types B and D. I will use this correspondence in type D to compute μ-values involving bad elements. I will conclude by showing that μ(x, w) is 0 or 1 when x is fully commutative in type D.
Gern, Tyson Charles, "Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D" (2013). Mathematics Graduate Theses & Dissertations. 26.