Twist formulas for one-row colored A2 webs and 5(3 tails of (2,2m)-torus links

Abstract

The ⁵ᶦ³ colored Jones polynomial J⁵ᶦ³ (L) is obtained by coloring the link components with two-row Young diagram λ. Although it is difficult to compute .J⁵ᶦ³(L) in general, we can calculate it by using Kuperberg's A₂ skein relation. In this paper, we show some formulas for twisted two strands colored by one-row Young diagram in A₂ web space and compute J⁵ᶦ³(T(2. 2m)) for an oriented (2. 2m) -torus link. These explicit formulas derives the 5l3 tail of T(2. 2m). They also give explicit descriptions of the 5l3 false theta series with one-row coloring because the 5l3 tail of T (2. 2m) is known as the false theta series.