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gln-webs, categorification and Khovanov-Rozansky homologies


Tubbenhauer, Daniel (2020). gln-webs, categorification and Khovanov-Rozansky homologies. Journal of Knot Theory and Its Ramifications, 29(11):1-96.

Abstract

In this paper we define an explicit basis for the gln-web algebra Hn(k⃗ ) (the gln generalization of Khovanov's arc algebra) using categorified q-skew Howe duality.
Our construction is a gln-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 Hn(k⃗ ), and it gives an explicit graded cellular basis of the 2-hom space between two gln-webs. We use this to give a (in principle) computable version of colored Khovanov-Rozansky gln-link homology, obtained from a complex defined purely combinatorially via the (thick cyclotomic) KLR algebra and needs only F.

Abstract

In this paper we define an explicit basis for the gln-web algebra Hn(k⃗ ) (the gln generalization of Khovanov's arc algebra) using categorified q-skew Howe duality.
Our construction is a gln-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 Hn(k⃗ ), and it gives an explicit graded cellular basis of the 2-hom space between two gln-webs. We use this to give a (in principle) computable version of colored Khovanov-Rozansky gln-link homology, obtained from a complex defined purely combinatorially via the (thick cyclotomic) KLR algebra and needs only F.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Language:English
Date:2020
Deposited On:15 Nov 2021 08:48
Last Modified:26 Apr 2024 01:35
Publisher:World Scientific Publishing
ISSN:0218-2165
OA Status:Closed
Publisher DOI:https://doi.org/10.1142/S0218216520500741
Related URLs:https://arxiv.org/abs/1404.5752
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