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The generalized lifting property of Bruhat intervals

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Abstract

In Tsukerman and Williams (Adv Math 285: 766–810, 2015), it is shown that every Bruhat interval of the symmetric group satisfies the so-called generalized lifting property. In this paper, we show that a Coxeter group satisfies this property if and only if it is finite and simply-laced.

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Acknowledgments

A huge gratitude goes to an anonymous referee who gave us the key idea for the proof of Theorem 3.5 and Proposition 3.6 avoiding the use of the classification theorem for finite Coxeter groups that was needed in a previous version of the manuscript.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126, Bologna, Italy

    Fabrizio Caselli

  2. Departamento de Matemáticas, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago, Chile

    Paolo Sentinelli

Authors
  1. Fabrizio Caselli
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  2. Paolo Sentinelli
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Corresponding author

Correspondence to Fabrizio Caselli.

Additional information

Paolo Sentinelli was supported by MIUR grant FIRB-RBFR12RA9W-002 “Perspectives in Lie theory”.

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Caselli, F., Sentinelli, P. The generalized lifting property of Bruhat intervals. J Algebr Comb 45, 687–700 (2017). https://doi.org/10.1007/s10801-016-0721-7

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  • DOI: https://doi.org/10.1007/s10801-016-0721-7

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