Schubert Calculus and Schur Functions

  • Hung-Hsi Wu
Part of the The University Series in Mathematics book series (USMA)


Given two Schubert cycles of a Grassmann manifold,σ a and σ b , we have the product formula
$${{\sigma }_{a}}\centerdot {{\sigma }_{b}}=\sum\limits_{c}{\delta \left( a,b,c \right)}{{\sigma }_{c}}.$$
The method for calculating δ(a,b,c) has already been given in a previous work [5] with the aid of Schur functions in the representation theory of the unitary group. On this basis of [5], making use of the similarity between the Schubert calculus and Schur functions and the branching formula of group representation theory, we investigate the question as to which of those can make σ c take δ(a,b,c) as coefficients in σ a σ b for given σ c ,σ b .


Irreducible Representation Unitary Group Irreducible Character Young Tableau Product Formula 
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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Hung-Hsi Wu
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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