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Involution products in Coxeter groups

By Sarah Hart and P.J. Rowley

Abstract

For W a Coxeter group, let\ud \ud = {w ∈ W | w = xy where x, y ∈ W and x 2 = 1 = y 2}.\ud \ud It is well known that if W is finite then W = . Suppose that w ∈ . Then the minimum value of ℓ(x) + ℓ(y) – ℓ(w), where x, y ∈ W with w = xy and x 2 = 1 = y 2, is called the excess of w (ℓ is the length function of W). The main result established here is that w is always W-conjugate to an element with excess equal to zero

Topics: ems
Publisher: de Gruyter
Year: 2011
OAI identifier: oai:eprints.bbk.ac.uk.oai2:811

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Citations

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