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Like all other knot polynomials, the superpolynomials should be defined inarbitrary representation R of the gauge group in (refined) Chern-Simons theory.However, not a single example is yet known of a superpolynomial beyondsymmetric or antisymmetric representations. We consider the expansion of thesuperpolynomial around the special polynomial in powers of (q-1) and (t-1) andsuggest a simple formula for the first-order deviation, which is presumablyvalid for arbitrary representation. This formula can serve as a crucial lackingtest of various formulas for non-trivial superpolynomials, which will appear inthe literature in the near future.

The first-order deviation of superpolynomial in an arbitrary representation from the special polynomial