• MIKE ROTHEmail author


In this note we show that when G is a classical semi-simple algebraic group, B ⊂ G a Borel subgroup, and X = G/B, then the structure coefficients of the Belkale–Kumar product ⨀0 on H*(X, Z) are all either 0 or 1.


Cohomology of homogeneous spaces roots and weights 


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  1. [BB]
    S. Billey, T. Braden, Lower bounds for Kazhdan–Lusztig polynomials from patterns, Transform. Groups 8 (2003), no. 4, 321–332.MathSciNetCrossRefGoogle Scholar
  2. [BK]
    P. Belkale, S. Kumar, Eigenvalue problem and a new product in cohomology of flag varieties, Invent. Math. 166 (2006), 185–228.MathSciNetCrossRefGoogle Scholar
  3. [BK2]
    P. Belkale, S. Kumar, Private communication.Google Scholar
  4. [Dix]
    J. Dixmier, Enveloping Algebras, Graduate Studies in Mathematics, Vol. 11, American Mathematical Society, Providence, RI, 1996.Google Scholar
  5. [D-W]
    R. Dewji, I. Dimitrov, A. McCabe, M. Roth, D. Wehlau, J. Wilson, Decomposing inversion sets of permutations and applications to faces of the Littlewood–Richardson cone, J. Algebraic Comb. 45 (2017), no. 4, 1173–1216.MathSciNetCrossRefGoogle Scholar
  6. [DR]
    I. Dimitrov, M. Roth, Cup products of line bundles on homogeneous varieties and generalized PRV components of multiplicity one, Algebra & Number Theory 11 (2017), no. 4, 767–815.MathSciNetCrossRefGoogle Scholar
  7. [Ko]
    B. Kostant, Lie algebra cohomology and the generalized Borel–Weil theorem, Ann. of Math. (2) 74 (1961), 329–387.MathSciNetCrossRefGoogle Scholar
  8. [L]
    H.-F. Lai, On the topology of the even-dimensional complex quadrics, Proc. Amer. Math. Soc. 46 (1974), 419–425.MathSciNetCrossRefGoogle Scholar
  9. [Re1]
    N. Ressayre, Multiplicative formulas in Schubert calculus and quiver representation, Indag. Math. (N.S.) 22 (2011), no. 1–2, 87–102.MathSciNetCrossRefGoogle Scholar
  10. [Re2]
    N. Ressayre, Geometric invariant theory and generalized eigenvalue problem II, Annales de l'Institute Fourier 61 (2011), n°4, 1467–1491.Google Scholar
  11. [Ri1]
    E. Richmond, A partial Horn recursion in the cohomology of flag varieties, J. Algebraic Combin. 30 (2009), no. 1, 1–17.MathSciNetCrossRefGoogle Scholar
  12. [Ri2]
    E. Richmond, A multiplicative formula for structure constants in the cohomology of flag varieties, Michigan Math. J. 61 (2012), no. 1, 3–17.MathSciNetCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada

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