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    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.

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    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.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 05 Oct 2022 12:58
    Last Modified: 06 Oct 2022 14:02
    URI: https://eprints.bbk.ac.uk/id/eprint/49281

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