We establish a correspondence between the SU(2) Witten–Reshetikhin–Turaev invariant for the Seifert manifold M(p1, p2, p3) and Ramanujan’s mock theta functions.

(3) T (n) = 1 2 (−1) L(−2 n − 1, χ12) where χ12(n) is the Dirichlet character with modulus 12 defined by n mod 12 1 5 7 11 others χ12(n) 1 −1 −1 1 0 It was pointed out that the right hand side of eq.… (More)

After Jones polynomial was introduced [1], studies of quantum invariants have been extensively developed. These quantum knot invariants are physically interpreted as the Feynman path integral of the… (More)

We study the knot invariant based on the quantum dilogarithm function. This invariant can be regarded as a non-compact analogue of Kashaev’s invariant, or the colored Jones invariant, and is defined… (More)

We study the Witten–Reshetikhin–Turaev SU(2) invariant for the Seifert manifolds S/Γ where Γ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler… (More)

Degeneracy patterns and hyper-multiplet structure in the spectrum of the su(m|n) supersymmetric Polychronakos spin chain are studied by use of the “motif”. Using the recursion relation of the… (More)

We consider an asymptotic expansion of Kashaev’s invariant or of the colored Jones function for the torus link T (2, 2m). We shall give q-series identity related to these invariants, and show that… (More)

The N-colored Jones polynomial JK (N) is one of the quantum invariants for knot K . It is associated with the N-dimensional irreducible representation of sl(2), and is powerful to classify knots.… (More)