Schubert Calculus and Threshold Polynomials of Affine Fusion

Details Schubert Calculus and Threshold Polynomials of Affine Fusion Schubert Calculus and Threshold Polynomials of Affine Fusion

2000-04-07

arxiv.org/abs/hep-th/0004055v2

Nucl.Phys. B584 (2000) 795-809

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 0 figures, harvmac, typos corrected, references added

Scientific paper

10.1016/S0550-3213(00)00404-1

We show how the threshold level of affine fusion, the fusion of Wess-Zumino-Witten (WZW) conformal field theories, fits into the Schubert calculus introduced by Gepner. The Pieri rule can be modified in a simple way to include the threshold level, so that calculations may be done for all (non-negative integer) levels at once. With the usual Giambelli formula, the modified Pieri formula deforms the tensor product coefficients (and the fusion coefficients) into what we call threshold polynomials. We compare them with the q-deformed tensor product coefficients and fusion coefficients that are related to q-deformed weight multiplicities. We also discuss the meaning of the threshold level in the context of paths on graphs.

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