The Iwahori–Hecke algebra is a mathematical structure that arises in the study of representation theory, particularly in the representation theory of the symmetric group and related algebraic objects, such as Coxeter groups and reductive algebraic groups. ### Definition The Iwahori–Hecke algebra, often denoted as \( \mathcal{H} \), is an algebra associated with a Coxeter group.
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Over the polynomial parameter ring, the generic Hecke algebra has basis and multiplicationThe parameters must agree for conjugate simple generators; equivalently, together with the braid relations presents the algebra.