## Nagoya Mathematical Journal

### Quantum $(\mathfrak{sl}_{n},\wedge V_{n})$ link invariant and matrix factorizations

Yasuyoshi Yonezawa

#### Abstract

In this paper, we give a generalization of Khovanov-Rozansky homology. We define a homology associated to the quantum $(\mathfrak{sl}_{n},\wedge V_{n})$ link invariant, where $\wedge V_{n}$ is the set of fundamental representations of $U_{q}(\mathfrak{sl}_{n})$. 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.

#### Article information

Source
Nagoya Math. J., Volume 204 (2011), 69-123.

Dates
First available in Project Euclid: 5 December 2011

https://projecteuclid.org/euclid.nmj/1323107838

Digital Object Identifier
doi:10.1215/00277630-1431840

Mathematical Reviews number (MathSciNet)
MR2863366

Zentralblatt MATH identifier
1271.57033

#### Citation

Yonezawa, Yasuyoshi. Quantum $(\mathfrak{sl}_{n},\wedge V_{n})$ link invariant and matrix factorizations. Nagoya Math. J. 204 (2011), 69--123. doi:10.1215/00277630-1431840. https://projecteuclid.org/euclid.nmj/1323107838

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