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.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call