On the Kazhdan-Lusztig order on cells and families

Abstract

We consider the set Irr.W / of (complex) irreducible characters of a finite Coxeter groupW . The Kazhdan-Lusztig theory of cells gives rise to a partition of Irr.W / into "families" and to a natural partial order≤LR on these families. Following an idea of Spaltenstein, we show that ≤LR can be characterised (and effectively computed) in terms of standard operations in the character ring of W . If, moreover, W is theWeyl group of an algebraic group G, then ≤LR can be interpreted, via the Springer correspondence, in terms of the closure relation among the "special" unipotent classes of G. © Swiss Mathematical Society.