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A Littlewood-Richardson rule for Grassmannian permutations
Author(s):
Kevin
Purbhoo;
Frank
Sottile
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1875-1882.
MSC (2000):
Primary 14N15;
Secondary 05E10
Posted:
January 8, 2009
MathSciNet review:
2480266
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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:
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- [BS98]
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- I. Coskun, A Littlewood-Richardson rule for two-step flag varieties, manuscript, 2007.
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- W. Fulton, Young tableaux. With applications to representation theory and geometry, Cambridge University Press, Cambridge, 1997. MR 1464693 (99f:05119)
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- 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)
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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:
10.1090/S0002-9939-09-09637-3
PII:
S 0002-9939(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
Posted:
January 8, 2009
Additional Notes:
The work of the second author was supported by NSF CAREER grant DMS-0538734
Communicated by:
Jim Haglund
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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