Hecke Algebras
نویسنده
چکیده
which is Artin’s braid relation. In general we will refer to (1) as the braid relation satisfied by si and sj. In order for W to be a Coxeter group it is required that the given set of relations between elements of I give a presentation of W . Informally, this means that any relation between generators in I can be deduced from the fact that the s ∈ Σ have order 2 and the braid relations. Formally, it means the following. More formally, it means that W is isomorphic to the free group on r generators σ1, · · · , σr modulo the smallest normal subgroup containing σ i and (σiσj) . For example, the symmetric group Sr+1 is a Coxeter group with generators si = (i, i+ 1). If r = 2, we have a presentation in generators and relations:
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