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A Littlewood-Richardson rule for Grassmannian permutations


Authors: Kevin Purbhoo and Frank Sottile
Journal: Proc. Amer. Math. Soc. 137 (2009), 1875-1882
MSC (2000): Primary 14N15; Secondary 05E10
DOI: https://doi.org/10.1090/S0002-9939-09-09637-3
Published electronically: January 8, 2009
MathSciNet review: 2480266
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a combinatorial rule for computing intersection numbers on a flag manifold which come from products of Schubert classes pulled back from Grassmannian projections. This rule generalizes the known rule for Grassmannians.


References [Enhancements On Off] (What's this?)

  • [BS98] N. Bergeron and F. Sottile, Schubert polynomials, the Bruhat order, and the geometry of flag manifolds, Duke Math. J. 95 (1998), no. 2, 373-423. MR 1652021 (2000d:05127)
  • [Co07] I. Coskun, A Littlewood-Richardson rule for two-step flag varieties, manuscript, 2007.
  • [Ful97] W. Fulton, Young tableaux. With applications to representation theory and geometry, Cambridge University Press, Cambridge, 1997. MR 1464693 (99f:05119)
  • [Knu00] A. Knutson, Descent-cycling in Schubert calculus, Experiment. Math. 10 (2001), no. 3, 345-353. MR 1917423 (2003g:14075)
  • [Kog01] M. Kogan, RC-graphs and a generalized Littlewood-Richardson rule, Internat. Math. Res. Notices (2001), no. 15, 765-782. MR 1849481 (2002m:05197)
  • [Mon59] D. Monk, The geometry of flag manifolds, Proc. London Math. Soc. (3) 9 (1959), 253-286. MR 0106911 (21:5641)
  • [RSSS06] J. Ruffo, Y. Sivan, E. Soprunova, and F. Sottile, Experimentation and conjectures in the real Schubert calculus for flag manifolds, Experiment. Math. 15 (2006), no. 2, 199-221. MR 2253007 (2007g:14066)
  • [Sot96] F. Sottile, Pieri's formula for flag manifolds and Schubert polynomials, Ann. Inst. Fourier (Grenoble) 46 (1996), no. 1, 89-110. MR 1385512 (97g:14035)
  • [Sta00] R. P. Stanley, Positivity problems and conjectures in algebraic combinatorics, Mathematics: Frontiers and perspectives, Amer. Math. Soc., Providence, RI, 2000, pp. 295-319. MR 1754784 (2001f:05001)

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Additional Information

Kevin Purbhoo
Affiliation: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1 Canada
Email: kpurbhoo@math.uwaterloo.ca

Frank Sottile
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: sottile@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9939-09-09637-3
Keywords: Flag manifold, Grassmannian, Littlewood-Richardson rule
Received by editor(s): September 14, 2007
Received by editor(s) in revised form: May 2, 2008
Published electronically: January 8, 2009
Additional Notes: The work of the second author was supported by NSF CAREER grant DMS-0538734
Communicated by: Jim Haglund
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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