The recursive nature of cominuscule Schubert calculus

Advances in Mathematics

Volumn 217, Issue 5, 2008, Pages 1962-2004

  Purbhoo, Kevin ^a   Sottile, Frank ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Cominuscule flag variety; Grassmannian; Horn inequalities; Littlewood Richardson rule; Schubert calculus

Indexed keywords

EID: 38849089209     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2007.09.010     Document Type: Article

References (28)

1. 1 - S for S a finite set. Compos. Math. 129 1 (2001) 67-86
2. Belkale P. Geometric proofs of Horn and saturation conjectures. J. Algebraic Geom. 15 1 (2006) 133-173
3. Belkale P., and Kumar S. Eigenvalue problem and a new product in cohomology of flag varieties. Invent. Math. 166 1 (2006) 185-228
4. Billey S., and Braden T. Lower bounds for Kazhdan-Lusztig polynomials from patterns. Transform. Groups 8 4 (2003) 321-332
5. Borel A. Linear Algebraic Groups. Grad. Texts in Math. vol. 126 (1991), Springer-Verlag
6. Chevalley C. Sur les décompositions cellulaires des espaces G / B. In: Haboush W. (Ed). Algebraic Groups and Their Generalizations: Classical Methods. Proc. Sympos. Pure Math. vol. 56, Part 1 (1994), Amer. Math. Soc. 1-23
7. Fulton Wm. Eigenvalues of sums of Hermitian matrices (after A. Klyachko). Séminaire Bourbaki, vol. 1997/98. Astérisque 252 (1998) 255-269 Exp. No. 845, 5
8. Fulton Wm. Eigenvalues, invariant factors, highest weights, and Schubert calculus. Bull. Amer. Math. Soc. (N.S.) 37 3 (2000) 209-249 (electronic)
9. Fulton Wm. Eigenvalues of majorized Hermitian matrices and Littlewood-Richardson coefficients. Linear Algebra Appl. 319 1-3 (2000) 23-36
10. Fulton Wm., and Harris J. Representation Theory. Grad. Texts in Math. vol. 129 (1991), Springer-Verlag
11. Fulton Wm., and Pragacz P. Schubert Varieties and Degeneracy Loci. Lecture Notes in Math. vol. 1689 (1998), Springer-Verlag, Berlin
12. Horn A. Eigenvalues of sums of Hermitian matrices. Pacific J. Math. 12 (1962) 225-241
13. Humphreys J. Introduction to Lie Algebras and Representation Theory (1972), Springer-Verlag, New York
14. Kleiman S.L. The transversality of a general translate. Compos. Math. 28 (1974) 287-297
15. Klyachko A.A. Stable bundles, representation theory, and Hermitian operators. Selecta Math. 4 (1998) 419-445
16. n (C) tensor products, I. Proof of the saturation conjecture. J. Amer. Math. Soc. 12 4 (1999) 1055-1090
17. n (C) tensor products, II. Puzzles determine facets of the Littlewood-Richardson cone. J. Amer. Math. Soc. 17 1 (2004) 19-48 (electronic)
18. Landsberg J.M., and Manivel L. On the projective geometry of rational homogeneous varieties. Comment. Math. Helv. 78 1 (2003) 65-100
19. Proctor R. Bruhat lattices, plane partition generating functions, and minuscule representations. European J. Combin. 5 4 (1984) 331-350
20. K. Purbhoo, Two step flag manifolds and the Horn conjecture, arXiv preprint math.AG/0603131
21. K. Purbhoo, Vanishing and non-vanishing criteria for branching Schubert calculus, PhD thesis, Berkeley, 2004, http://www.math.uwaterloo.ca/~kpurbhoo/papers/thesis.pdf
22. Richardson R., Röhrle G., and Steinberg R. Parabolic subgroups with abelian unipotent radical. Invent. Math. 110 3 (1992) 649-671
23. Röhrle G. On the structure of parabolic subgroups in algebraic groups. J. Algebra 157 1 (1993) 80-115
24. Serre J.-P. Algèbres de Lie semi-simples complexes (1966), W.A. Benjamin, Inc., New York
25. Stanley R. Two poset polytopes. Discrete Comput. Geom. 1 (1986) 9-23
26. Stanley R. Enumerative Combinatorics, vol. 1 (1997), Cambridge University Press, Cambridge with a foreword by Gian-Carlo Rota, corrected reprint of the 1986 original
27. H. Thomas, A. Yong, A combinatorial rule for (co)minuscule Schubert calculus, math.AG/0608276
28. Zelevinsky A. Littlewood-Richardson semigroups. New Perspectives in Algebraic Combinatorics. Berkeley, CA, 1996-1997. Math. Sci. Res. Inst. Publ. vol. 38 (1999), Cambridge Univ. Press, Cambridge 337-345