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The actions ofS n+1 andS n on the cohomology ring of a coxeter arrangement of typeA n−1

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Abstract

Let\(\mathcal{A}_{n - 1} \subset \mathbb{C}^{n - 1} \) be the complexified Coxeter arrangement of hyperplanes of typeA n−1. In this paper we construct anS n+1 extension of the naturalS n action on the complex cohomology ring of the complement ofA n−1. Recurrence formulas connecting characters with respect to theS n and theS n+1 action are given.

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References

  1. V.I. Arnold, The cohomology ring of the coloured braid group. Mat. Zametki 5, 227–231 (1969); Math. Notes 5, 138–140 (1969)

    MathSciNet  Google Scholar 

  2. E. Brieskorn, Sur les groupes de tresses. In: Séminaire Bourbaki 1971/72. Lecture Notes in Math. 317, Springer Verlag, 1973, 21–24

  3. G.I. Lehrer, On the Poincaré series associated with Coxeter group actions on complements of hyperplanes. J. London Math. Soc. (2) 36, 275–294 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  4. G.I. Lehrer, A toral configuration space and regular semisimple conjugacy classes. Math. Proc. Cam. Phil. Soc. 118, 105–113 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. G.I. Lehrer, L. Solomon, On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes. J. Algebra 104, 410–424 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. O. Mathieu, Hidden ∑n+1-actions. Commun. Math. Phys. 176, 467–474 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Orlik, L. Solomon, Combinatorics and topology of complements of hyperplanes. Inventh. Math. 56, 167–189 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  8. P. Orlik, H. Terao, Arrangements of hyperplanes. Berlin, New York: Springer 1992

    MATH  Google Scholar 

  9. A. Robinson, S. Whitehouse, The tree representation of ∑n+1. To appear in J. Pure App. Alg.

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  1. Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, Italia

    Giovanni Gaiffi

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  1. Giovanni Gaiffi
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Gaiffi, G. The actions ofS n+1 andS n on the cohomology ring of a coxeter arrangement of typeA n−1 . Manuscripta Math 91, 83–94 (1996). https://doi.org/10.1007/BF02567941

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  • DOI: https://doi.org/10.1007/BF02567941

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