61 research outputs found
The foam and the matrix factorization sl3 link homologies are equivalent
We prove that the foam and matrix factorization universal rational sl3 link
homologies are naturally isomorphic as projective functors from the category of
link and link cobordisms to the category of bigraded vector spaces.Comment: We have filled a gap in the proof of Lemma 5.2. 28 page
Categorified skew Howe duality and comparison of knot homologies
In this paper, we show an isomorphism of homological knot invariants
categorifying the Reshetikhin-Turaev invariants for . Over the
past decade, such invariants have been constructed in a variety of different
ways, using matrix factorizations, category , affine
Grassmannians, and diagrammatic categorifications of tensor products.
While the definitions of these theories are quite different, there is a key
commonality between them which makes it possible to prove that they are all
isomorphic: they arise from a skew Howe dual action of for
some . In this paper, we show that the construction of knot homology
based on categorifying tensor products (from earlier work of the second author)
fits into this framework, and thus agrees with other such homologies, such as
Khovanov-Rozansky homology. We accomplish this by categorifying the action of
on
using
diagrammatic bimodules. In this action, the functors corresponding to
and are quite different in nature, but
they will switch roles under Koszul duality.Comment: 62 pages. preliminary version, comments welcom
Operadores de Yang-Baxter e a categoria dos emaranhados
Trabalho de síntese para efeitos de preparação de provas de aptidão pedagógica e capacidade científica, Matemática, Unidade de Ciências Exactas e Humanas, Universidade do Algarve, 1998Todos nós conhecemos o famoso truque do prestidigitador: mostra uma corda com um grande nó no meio e de repente puxa as duas pontas da corda cada uma para o seu lado e o nó desaparece misteriosamente
A diagrammatic categorification of the q-Schur algebra
In this paper we categorify the q-Schur algebra S(n,d) as a quotient of
Khovanov and Lauda's diagrammatic 2-category U(sln). We also show that our
2-category contains Soergel's monoidal category of bimodules of type A, which
categorifies the Hecke algebra H(d), as a full sub-2-category if d does not
exceed n. For the latter result we use Elias and Khovanov's diagrammatic
presentation of Soergel's monoidal category of type A.Comment: 60 pages, lots of figures. v3: Substantial changes. To appear in
Quantum Topolog
TheslN-web algebras and dual canonical bases
In this paper, which is a follow-up to [38], I define and study SIN-web algebras, for any N >= 2. For N = 2 these algebras are isomorphic to Khovanov's [22] arc algebras and for N = 3 they are Morita equivalent to the sl(3)-web algebras which I defined and studied together with Pan and Tubbenhauer [34]. The main result of this paper is that the SIN-web algebras are Morita equivalent to blocks of certain level-N cyclotomic KLR algebras, for which I use the categorified quantum skew Howe duality defined in [38]. Using this Morita equivalence and Brundan and Kleshchev's [4] work on cyclotomic KLR-algebras, I show that there exists an isomorphism between a certain space of SIN-webs and the split Grothendieck group of the corresponding SIN-web algebra, which maps the dual canonical basis elements to the Grothendieck classes of the indecomposable projective modules (with a certain normalization of their grading).info:eu-repo/semantics/publishedVersio
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