A Recursive Rule for Kazhdan–Lusztig Characters

Induction and Restriction of Kazhdan–Lusztig Cells

“…In this paper we show that a generalized Littlewood Richardson rule implies a recursion theorem for the Kazhdan Lusztig characters of arbitrary Coxeter groups. This result explains and generalizes the recursion, which was found by direct calculations in [Ro,Theorem 1].…”

“…This theorem generalizes the recursive part of [Ro,Theorem 1]. The following corollary is immediate.…”

“…By considering a Littlewood Richardson type rule for Kazhdan Lusztig representations we obtain a far reaching generalization of the main result of [Ro]. Unfortunately, the new approach does not suggest an analogue to the explicit coefficients, which were calculated in [Ro,Theorem 2].…”

Power Sum Expansion of Chromatic Quasisymmetric Functions

“…We denote by U α the set of α-unimodal subsets of [n − 1]. The following statement is a special case of [2,Theorem 4].…”

“…Our main result (Theorem 3.1) is formulated and proven in Section 3, after background material has been reviewed in Section 2. The result is derived from the expansion of X G in the basis of fundamental quasisymmetric functions [4, Theorem 3.1] via a formula of Roichman [2] for the irreducible characters of the symmetric group (the proof is motivated by the discussion of character formulas and distributions of descent sets in [1,Section 6]). Section 4 exploits a known bijection [9] between certain permutations of a partially ordered set P and acyclic orientations of the incomparability graph of P to provide an alternative formulation (Corollary 4.2) of the main result.…”