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Higher Bruhat orders and relations in the braid groups

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Abstract

We prove relations in the braid group that generalize the relations of the formaba=bab. These relations are obtained by means of the generalization to the higher Bruhat orders of the well-known relation between the decompositions of the element of maximal length in the Weyl groupA n−1 and some specific linear orders on the system of positive roots ofA n−1 .

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Authors and Affiliations

  1. Kolomna Pedagogical Institute, USSR

    G. G. Il’yuta

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  1. G. G. Il’yuta
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Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 840–848, December, 1999.

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Il’yuta, G.G. Higher Bruhat orders and relations in the braid groups. Math Notes 66, 694–700 (1999). https://doi.org/10.1007/BF02674326

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  • DOI: https://doi.org/10.1007/BF02674326

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