Matrix factorizations and intertwiners of the fundamental representations of quantum group U_q (sl_n)

Abstract

We want to construct a homological link invariant whose Euler characteristic is MOY polynomial as Khovanov and Rozansky constructed a categorification of HOMFLY polynomial. The present paper gives the first step to construct a categorification of MOY polynomial. For the essential colored planar diagrams with additional data which is a sequence naturally induced by coloring, we define matrix factorizations, and then we define a matrix factorization for planar diagram obtained by gluing the essential colored planar diagrams as tensor product of the matrix factorizations for the essential planar diagrams. Moreover, we show that some matrix factorizations deribed from tensor product of the essential matrix factorizations have homotopy equivalences corresponding to MOY relations.

37 pages

References in corpus (5)

• Khovanov's homology for tangles and cobordisms
• Note on Khovanov link cohomology
• Some differentials on Khovanov-Rozansky homology
• Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
• Matrix factorizations and colored MOY graphs

Cited by in corpus (8)

• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• sl(N)-Web categories
• A diagrammatic categorification of the q-Schur algebra
• Matrix factorizations and colored MOY graphs
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• The sl(N)-web algebras and dual canonical bases
• The Khovanov-Lauda 2-category and categorifications of a level two quantum sl(n) representation
• The 1,2-coloured HOMFLY-PT link homology