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17. Schubert Calculus and Schur Functions

Author

Hung-Hsi Wu

Subjects
Physics, Combinatorics, Irreducible representation, Product (mathematics), Schubert calculus, Schur's lemma, Young tableau, Schubert polynomial, Schur algebra, Topology, Schur's theorem
Abstract

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 .

Published
1991

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