Abstract
We consider the set Irr(W) of (complex) irreducible characters of a finite Coxeter group W. The Kazhdan–Lusztig theory of cells gives rise to a partition of Irr(W) into “families” and to a natural partial order $\leq\_{\mathcal{LR}}$ on these families. Following an idea of Spaltenstein, we show that $\leq\_{\mathcal{LR}}$ can be characterised (and effectively computed) in terms of standard operations in the character ring of W. If, moreover, W is the Weyl group of an algebraic group G, then $\leq\_{\mathcal{LR}}$ can be interpreted, via the Springer correspondence, in terms of the closure relation among the “special” unipotent classes of G.
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