On colored HOMFLY polynomials for twist knots

Abstract

Recent results of J.Gu and H.Jockers provide the lacking initial conditions for the evolution method in the case of the first non-trivially colored HOMFLY polynomials H_{[21]} for the family of twist knots. We describe this application of the evolution method, which finally allows one to penetrate through the wall between (anti)symmetric and non-rectangular representations for a whole family. We reveal the necessary deformation of the differential expansion, what, together with the recently suggested matrix model approach gives new opportunities to guess what it could be for a generic representation, at least for the family of twist knots.

8 pages

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Cited by in corpus (7)

• On colored HOMFLY polynomials for twist knots
• Differential expansion for link polynomials
• On R-matrix approaches to knot invariants
• Extension of KNTZ trick to non-rectangular representations
• Integrality structures in topological strings I: framed unknot
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• HOMFLY Polynomials of Pretzel Knots