Lengths of Involutions in Finite Coxeter Groups

Hart, Sarah and Rowley, Peter (2023) Lengths of Involutions in Finite Coxeter Groups. Journal of Pure and Applied Algebra 227 (2), p. 107190. ISSN 0022-4049.

Abstract

Let W be a finite Coxeter group and X a subset of W . The length polynomial L_W,X (t) is defined by L_W,X (t) = ∑ x∈X t^{l(x)}, where l is the length function on W. If X = {x ∈ W : x^2 = 1} then we call L_W,X(t) the involution length polynomial of W . In this article we derive expressions for the length polynomial where X is any conjugacy class of involutions, and the involution length polynomial, in any finite Coxeter group W . In particular, these results correct errors in the literature for the involution length polynomials of Coxeter groups of type Bn and Dn.

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