Twist Formulas for One-Row Colored A2 Webs and $\mathfrak {s}\mathfrak {l}_{3}$ Tails of (2, 2m)-Torus Links
Tóm tắt
The
$\mathfrak {s}\mathfrak {l}_{3}$
colored Jones polynomial
$J_{\lambda }^{\mathfrak {s}\mathfrak {l}_{3}}(L)$
is obtained by coloring the link components with two-row Young diagram λ. Although it is difficult to compute
$J_{\lambda }^{\mathfrak {s}\mathfrak {l}_{3}}(L)$
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
$J_{(n,0)}^{\mathfrak {s}\mathfrak {l}_{3}}(T(2,2m))$
for an oriented (2,2m)-torus link. These explicit formulas derives the
$\mathfrak {s}\mathfrak {l}_{3}$
tail of T(2,2m). They also give explicit descriptions of the
$\mathfrak {s}\mathfrak {l}_{3}$
false theta series with one-row coloring because the
$\mathfrak {s}\mathfrak {l}_{2}$
tail of T(2,2m) is known as the false theta series.
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