𝔤𝔩n-webs, categorification and Khovanov–Rozansky homologies
- Tubbenhauer, Daniel ORCID D.T.Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, Campus Irchel, Office Y27J32, CH-8057 Zürich, Switzerland
- 2020-11-5
Published in:
- Journal of Knot Theory and Its Ramifications. - World Scientific Pub Co Pte Lt. - 2020, p. 2050074
English
In this paper, we define an explicit basis for the [Formula: see text]-web algebra [Formula: see text] (the [Formula: see text] generalization of Khovanov’s arc algebra) using categorified [Formula: see text]-skew Howe duality. Our construction is a [Formula: see text]-web version of Hu–Mathas’ graded cellular basis and has two major applications: it gives rise to an explicit isomorphism between a certain idempotent truncation of a thick calculus cyclotomic KLR algebra and [Formula: see text], and it gives an explicit graded cellular basis of the [Formula: see text]-hom space between two [Formula: see text]-webs. We use this to give a (in principle) computable version of colored Khovanov–Rozansky [Formula: see text]-link homology, obtained from a complex defined purely combinatorially via the (thick cyclotomic) KLR algebra and needs only [Formula: see text].
- Language
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- English
- Open access status
- green
- Identifiers
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- DOI 10.1142/s0218216520500741
- ISSN 0218-2165
- Persistent URL
- https://sonar.ch/global/documents/41854
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