Loading...
30 results
Search Results
Now showing 1 - 10 of 30
- The universal sl(3)-link homologyPublication . Mackaay, Marco; Vaz, PedroWe 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.
- Trihedral Soergel bimodulesPublication . Mackaay, Marco; Mazorchuk, Volodymyr; Miemietz, Vanessa; Tubbenhauer, DanielThe quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum sl(2) representation category. It also establishes a precise relation between the simple transitive 2-representations of both monoidal cate-gories, which are indexed by bicolored ADE Dynldn diagrams. Using the quantum Satake correspondence between affine A(2) Soergel bimodules and the semisimple quotient of the quantum sl(3)representation category, we introduce trihedral Hecke algebras and Soergel bimodules, generalizing dihedral Hecke algebras and Soergel bimodules. These have their own Kazhdan-Lusztig combinatorics, simple transitive 2-representations corresponding to tricolored generalized ADE Dynkin diagrams.
- Analogues of centralizer subalgebras for fiat 2-categories and their 2-representationsPublication . Mackaay, Marco; Mazorchuk, Volodymyr; Miemietz, Vanessa; Zhang, XiaotingThe main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex J of a fiat 2-category C and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of C associated with a diagonal H-cell in J. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types B-3 and B-4.
- Simple transitive $2$-representations of Soergel bimodules for finite Coxeter typesPublication . Mackaay, Marco; Mazorchuk, Volodymyr; Miemietz, Vanessa; Tubbenhauer, Daniel; Zhang, XiaotingIn this paper we show that Soergel bimodules for finite Coxeter types have only finitely many equivalence classes of simple transitive $2$-representations and we complete their classification in all types but $H_{3}$ and $H_{4}$.
- Categorifications of the extended affine Hecke algebra and the affine q-Schur algebra S(n, r) for 3 <= r < nPublication . Mackaay, Marco; Thiel, Anne-LaureWe categorify the extended affine Hecke algebra and the affine quantum Schur algebra S(n, r) for 3 <= r < n, using results on diagrammatic categorification in affine type A by Elias-Williamson, that extend the work of Elias-Khovanov for finite type A, and Khovanov-Lauda respectively. We also define 2-representations of these categorifications on an extension of the 2-category of affine (singular) Soergel bimodules. These results are the affine analogue of the results in [28].
- Erratum - A remark on Rasmussen's Invariant of knots (vol 16, pg 333, 2007)Publication . Mackaay, Marco; Turner, P.; Vaz, P.
- The foam and the matrix factorization sl(3) link homologies are equivalentPublication . Mackaay, Marco; Vaz, PedroWe prove that the universal rational sl(3) link homologies which were constructed by Khovanov in [3] and the authors in [7], using foams, and by Khovanov and Rozansky in [4], using matrix factorizations, are naturally isomorphic as projective functors from the category of links and link cobordisms to the category of bigraded vector spaces.
- A remark on Rasmussen's invariant of knotsPublication . Mackaay, Marco; Turner, Paul; Vaz, PedroWe show that Rasmussen's invariant of knots, which is derived from Lee's variant of Khovanov homology, is equal to an analogous invariant derived from certain other filtered link homologies.
- Holonomy and parallel transport for Abelian gerbesPublication . Mackaay, Marco; Picken, R.In this paper, we establish a one-to-one correspondence between U(1)-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This result is a higher-order analogue of the familiar equivalence between bundles with connections and their holonomies for connected manifolds. The holonomy of a gerbe with group U(1) on a simply connected manifold M is a group morphism from the thin second homotopy group to U(1), satisfying a smoothness condition, where a homotopy between maps from [0,1](2) to M is thin when its derivative is of rank less than or equal to2. For the non-simply connected case, holonomy is replaced by a parallel transport functor between two special Lie groupoids, which we call Lie 2-groups. The reconstruction of the gerbe and connection from its holonomy is carried out in detail for the simply connected case. (C) 2002 Elsevier Science (USA).
- Operadores de Yang-Baxter e a categoria dos emaranhadosPublication . Mackaay, Marco; Marques, Maria da Graça RendeiroTodos 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.
- «
- 1 (current)
- 2
- 3
- »