Quantum (sln, ∧V n ) link invariant and matrix factorizations

By Yasuyoshi Yonezawa. Nagoya mathematical journal, 2009

49 citations recorded by the source corpus.

Abstract In this paper, we give a generalization of Khovanov-Rozansky homology. We define a homology associated to the quantum (sln, ∧Vn ) link invariant, where ∧Vn is the set of fundamental representations of Uq(sln ). In the case of an oriented link diagram composed of [k, 1]-crossings, we define a homology and prove that the homology is invariant under Reidemeister II and III moves. In the case of an oriented link diagram composed of general [i,j]-crossings, we define a normalized Poincaré polynomial of homology and prove that the normalized Poincaré polynomial is a link invariant.

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Citations in the corpus

Deformations of colored sl(N) link homologies via foams (2015, unknown): “This was later extended by Wu [43] and Yonezawa [44] to a categorified invariant of links whose components are colored by fundamental representations VkCN of slN for 0 k N .”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “For general sln, matrix factorizations become the primary computation tool [77, 76, 75], and the only way to evaluate a closed foam is through the mysterious Kapustin-Li formula [51, 23].”
A diagrammatic categorification of the q-Schur algebra (2010, background): “In the meanwhile, papers have appeared in which the colored HOMFLYPT homology has been constructed using matrix factorizations; see [40], [41], [42], [43], and [44].”