A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-
Simons theory with SU (N) gauge group is studied in symmetric approach. A special basis in …

A closed form expression for multiplicity-free quantum 6-j symbols (MFS) was proposed in [1]
for symmetric representations of U q (sl N), which are the simplest class of multiplicity-free …

We have recently proposed [1] a powerful method for computing group factors of the
perturbative series expansion of the Wilson loop in the Chern-Simons theory with SU (N) …

We present a new conjectural symmetry of the colored Alexander polynomial, that is the
specialization of the quantum sl _N sl N invariant widely known as the colored HOMFLY-PT …

We derive the analogues of the Harer-Zagier formulas for single-and double-trace
correlators in the q-deformed Hermitian Gaussian matrix model. This fully describes single …

We prove that normalized colored Alexander polynomial (the A→ 1 limit of colored HOMFLY-
PT polynomial) of a knot K evaluated for one-hook (L-shape) representation R possesses …

The defect of differential (cyclotomic) expansion for colored HOMFLY-PT polynomials is
conjectured to be invariant under any antiparallel evolution and change linearly with the …

We discuss different invariants of knots and links that depend on a primitive root of unity. We
clarify the definitions of existing invariants with the Reshetikhin–Turaev method, present the …

We prove that normalized colored Alexander polynomial (the $ A\rightarrow 1$ limit of
colored HOMFLY-PT polynomial) evaluated for one-hook (L-shape) representation R …

The construction known as Gauss diagrams or Gauss words is one of the oldest in knot
theory and has been studied extensively both in the context of knots and in the context of …