Y. Soibelman | Searcharxiv

arXiv2012

HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants

Hilbert scheme topological invariants of plane curve singularities are identified to framed threefold stable pair invariants. As a result, the conjecture of Oblomkov and Shende on HOMFLY polynomials of links of plane curve singularities is given a Calabi-Yau threefold interpretation. The motivic Donaldson-Thomas theory developed by M. Kontsevich and the third author then yields natural motivic invariants for algebraic knots. This construction is motivated by previous work of V. Shende, C. Vafa and the first author on the large $N$ duality derivation of the above conjecture.

math.AG↗

arXiv1995

Representations of Quantum Affine Algebras

In this paper we define a quantum version of the ``fusion'' tensor product of two representations of an affine Kac-Moody algebra.It is replaced by what we call fusion action of the category of finite-dimensional representations of quantum affine algebra on its highest weight representations. We construct a quantum version of the associativity constraint. We give categorical treatment of the subject and related questions ( like quantum Knizhnik-Zamolodchikov equations).

q-alg↗