Bijective Projections on Parabolic Quotients of Affine Weyl Groups

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  • Additional Information
    • Publication Date:
      2012
    • Collection:
      Mathematics
    • Abstract:
      Affine Weyl groups and their parabolic quotients are used extensively as indexing sets for objects in combinatorics, representation theory, algebraic geometry, and number theory. Moreover, in the classical Lie types we can conveniently realize the elements of these quotients via intuitive geometric and combinatorial models such as abaci, alcoves, coroot lattice points, core partitions, and bounded partitions. Berg, Jones, and Vazirani described a bijection between n-cores with first part equal to k and (n-1)-cores with first part less than or equal to k, and they interpret this bijection in terms of these other combinatorial models for the quotient of the affine symmetric group by the finite symmetric group. In this paper we discuss how to generalize the bijection of Berg-Jones-Vazirani to parabolic quotients of affine Weyl groups in type C. We develop techniques using the associated affine hyperplane arrangement to interpret this bijection geometrically as a projection of alcoves onto the hyperplane containing their coroot lattice points. We are thereby able to analyze this bijective projection in the language of various additional combinatorial models developed by Hanusa and Jones, such as abaci, core partitions, and canonical reduced expressions in the Coxeter group.
      Comment: 31 pages and 13 figures; background has been streamlined and exposition improved; to appear in J. Algebraic Combin
    • Accession Number:
      edsarx.1212.0771
  • Citations
    • ABNT:
      MILIĆEVIĆ, E. et al. Bijective Projections on Parabolic Quotients of Affine Weyl Groups. [s. l.], 2012. Disponível em: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1212.0771&custid=s6224580. Acesso em: 20 jan. 2020.
    • AMA:
      Milićević E, Nichols M, Park MH, Shi X, Youcis A. Bijective Projections on Parabolic Quotients of Affine Weyl Groups. 2012. http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1212.0771&custid=s6224580. Accessed January 20, 2020.
    • APA:
      Milićević, E., Nichols, M., Park, M. H., Shi, X., & Youcis, A. (2012). Bijective Projections on Parabolic Quotients of Affine Weyl Groups. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1212.0771&custid=s6224580
    • Chicago/Turabian: Author-Date:
      Milićević, Elizabeth, Margaret Nichols, Min Hae Park, XiaoLin Shi, and Alexander Youcis. 2012. “Bijective Projections on Parabolic Quotients of Affine Weyl Groups.” http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1212.0771&custid=s6224580.
    • Harvard:
      Milićević, E. et al. (2012) ‘Bijective Projections on Parabolic Quotients of Affine Weyl Groups’. Available at: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1212.0771&custid=s6224580 (Accessed: 20 January 2020).
    • Harvard: Australian:
      Milićević, E, Nichols, M, Park, MH, Shi, X & Youcis, A 2012, ‘Bijective Projections on Parabolic Quotients of Affine Weyl Groups’, viewed 20 January 2020, .
    • MLA:
      Milićević, Elizabeth, et al. Bijective Projections on Parabolic Quotients of Affine Weyl Groups. 2012. EBSCOhost, search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1212.0771&custid=s6224580.
    • Chicago/Turabian: Humanities:
      Milićević, Elizabeth, Margaret Nichols, Min Hae Park, XiaoLin Shi, and Alexander Youcis. “Bijective Projections on Parabolic Quotients of Affine Weyl Groups,” 2012. http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1212.0771&custid=s6224580.
    • Vancouver/ICMJE:
      Milićević E, Nichols M, Park MH, Shi X, Youcis A. Bijective Projections on Parabolic Quotients of Affine Weyl Groups. 2012 [cited 2020 Jan 20]; Available from: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1212.0771&custid=s6224580