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Cyclotomic expansions of colored $SU(n)$ invariants of two-strand torus knots and Bailey transforms
Habiro's cyclotomic expansion of the colored Jones polynomial has a higher rank analogue conjectured by Chen--Liu--Zhu for colored $SU(n)$ invariants. We prove this conjecture for torus knots $T(2,2p+1)$ and give a Bailey theoretic realization of the cyclotomic coefficients. For $n\geq2$ and $K_p=T(
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