If a knot is represented by an m‐strand braid, then HOMFLY polynomial in representation R
is a sum over characters in all representations Q∈ R⊗ m. Coefficients in this sum are traces …

A bstract The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-
Simons theory, possess an especially simple representation for torus knots, which begins …

A bstract Explicit answer is given for the HOMFLY polynomial of the figure eight knot 4 1 in
arbitrary symmetric representation R=[p]. It generalizes the old answers for p= 1 and 2 and …

A bstract We discuss the notion of renormalization group (RG) completion of non-Gaussian
Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in …

We explain how the calculations of [20], which provided the first evidence for non-trivial
structures of Gaussian correlators in tensor models, are efficiently performed with the help of …

A bstract\(\mathrm {\mathcal {R}}\)-matrix is explicitly constructed for simplest representations
of the Ding-Iohara-Miki algebra. Calculation is straightforward and significantly simpler than …

We discuss using the cabling procedure to calculate colored HOMFLY polynomials. We
describe how it can be used and how the projectors and R-matrices needed for this …

We discuss the recent proposal of arXiv: 1608.05351 about generalization of the RTT
relation to network matrix models. We show that the RTT relation in these models is modified …

This is a review of (q-) hypergeometric orthogonal polynomials and their relation to
representation theory of quantum groups, to matrix models, to integrable theory, and to knot …

A bstract With the help of the evolution method we calculate all HOMFLY polynomials in all
symmetric representations [r] for a huge family of (generalized) pretzel links, which are made …