We define the universal sl 3 -link homology, which depends on 3 parameters, following Khovanov's approach with foams. We show that this 3-parameter link homology, when taken with complex coefficients, can be divided into 3 isomorphism classes. The first class is the one to which Khovanov's original sl 3 -link homology belongs, the second is the one studied by Gornik in the context of matrix factorizations and the last one is new. Following an approach similar to Gornik's we show that this new link homology can be described in terms of Khovanov's original sl 2 -link homology.57M27; 57M25, 81R50, 18G60
Abstract. In this paper we categorify the q-Schur algebra S q .n; d / as a quotient of Khovanov and Lauda's diagrammatic 2-category U.sl n / [16]. We also show that our 2-category contains Soergel's [33] monoidal category of bimodules of type A, which categorifies the Hecke algebra H q .d /, as a full sub-2-category if d Ä n. For the latter result we use Elias and Khovanov's diagrammatic presentation of Soergel's monoidal category of type A; see [8].
Abstract. We use super q-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of gl N -modules (and, more generally, gl N |M -modules) whose objects are tensor generated by exterior and symmetric powers of the vector representations. As an application, we give a representation theoretic explanation and a diagrammatic version of a known symmetry of colored HOMFLY-PT polynomials.
Abstract. In this paper we define the 1,2-coloured HOMFLY-PT triply graded link homology and prove that it is a link invariant. We also conjecture on how to generalize our construction for arbitrary colours.
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