Grassmannian Cohomolgy Rings and Fusion Rings from Algebraic Equations

Details Grassmannian Cohomolgy Rings and Fusion Rings from Algebraic Equations Grassmannian Cohomolgy Rings and Fusion Rings from Algebraic Equations

1997-04-18

arxiv.org/abs/hep-th/9704138v2

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, LaTeX. Minor adjustment to references

Scientific paper

The potential that generates the cohomology ring of the Grassmannian is given in terms of the elementary symmetric functions using the Waring formula that computes the power sum of roots of an algebraic equation in terms of its coefficients. As a consequence, the fusion potential for $su(N)_K$ is obtained. This potential is the explicit Chebyshev polynomial in several variables of the first kind. We also derive the fusion potential for $sp(N)_K$ from a reciprocal algebraic equation. This potential is identified with another Chebyshev polynomial in several variables. We display a connection between these fusion potentials and generalized Fibonacci and Lucas numbers.

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