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VOLUME 97 (2013) | ISSUE 4 | PAGE 195
The first-order deviation of superpolynomial in an arbitrary representation from the special polynomial
DOI: 10.7868/S0370274X13040012
Abstract
Like all other knot polynomials, the superpolynomials should be defined in arbitrary representation R of the gauge group in (refined) Chern-Simons theory. However, not a single example is yet known of a superpolynomial beyond symmetric or antisymmetric representations. Following the article Equations on knot polynomials and 3d/5d duality, we consider the expansion of the superpolynomial around the special polynomial in powers of q-1 and t-1 and suggest a simple formula for the first-order deviation, which is presumably valid for arbitrary representation. This formula can serve as a crucial lacking test of various formulas for non-trivial superpolynomials, which will appear in the literature in the near future.