42 citations · 175 across the 18 of their papers we have counts for
19 papers
Type Webs
Elijah Bodish, Ben Elias, David E. V. Rose
We solve the type case of the main open problem from Kuperberg's 1996 paper "Spiders for rank 2 Lie algebras." That is, we define a -linear pivotal category $\ma…
Spin Link Homology
Elijah Bodish, Ben Elias, David E. V. Rose
We put a new spin on Khovanov--Rozansky homology. That is, we equip -colored Khovanov--Rozansky homology with an involution whose -eigenspaces are…
Bordered invariants from Khovanov homology
Matthew Hogancamp, David E. V. Rose, Paul Wedrich
To every compact oriented surface that is composed entirely out of 2-dimensional 0- and 1-handles, we construct a dg category using structures arising in Khovanov homology. These d…
A Kirby color for Khovanov homology
Matthew Hogancamp, David E. V. Rose, Paul Wedrich
We construct a Kirby color in the setting of Khovanov homology: an ind-object of the annular Bar-Natan category that is equipped with a natural handle slide isomorphism. Using func…
Categorification of the internal braid group action for quantum groups I: 2-functoriality
Michael T. Abram, Laffite Lamberto-Egan, Aaron D. Lauda +1
We define 2-functors on the categorified quantum group of a simply-laced Kac-Moody algebra that induce Lusztig's internal braid group action at the level of the Grothendieck group.
Decreasing subsequences and Viennot for oscillating tableaux
Elijah Bodish, Ben Elias, David E. V. Rose +1
We establish an extension of Viennot's geometric (shadow line) construction to the setting of oscillating tableaux. We then use this to give a new proof of the Type analogue of…
Link splitting deformation of colored Khovanov--Rozansky homology
Matthew Hogancamp, David E. V. Rose, Paul Wedrich
We introduce a multi-parameter deformation of the triply-graded Khovanov--Rozansky homology of links colored by one-column Young diagrams, generalizing the "-ified" link homolog…
A skein relation for singular Soergel bimodules
Matthew Hogancamp, David E. V. Rose, Paul Wedrich
We study the skein relation that governs the HOMFLYPT invariant of links colored by one-column Young diagrams. Our main result is a categorification of this colored skein relation.…
Type Webs
Elijah Bodish, Ben Elias, David E. V. Rose +1
We define a -linear pivotal category and prove that it is equivalent to the full subcategory of finite-dimensional representations…
On webs in quantum type
David E. V. Rose, Logan Tatham
We study webs in quantum type , focusing on the rank three case. We define a linear pivotal category diagrammatically by generators and relations…
HOMFLYPT homology for links in handlebodies via type A Soergel bimodules
David E. V. Rose, Daniel Tubbenhauer
We define a triply-graded invariant of links in a genus g handlebody, generalizing the colored HOMFLYPT (co)homology of links in the 3-ball. Our main tools are the description of t…
Annular Evaluation and Link Homology
Hoel Queffelec, David E. V. Rose, Antonio Sartori
We use categorical annular evaluation to give a uniform construction of both and HOMFLYPT Khovanov-Rozansky link homology, as well as annular versions of these th…
Sutured annular Khovanov-Rozansky homology
Hoel Queffelec, David E. V. Rose
We introduce an sl(n) homology theory for knots and links in the thickened annulus. To do so, we first give a fresh perspective on sutured annular Khovanov homology, showing that i…
Deformations of colored sl(N) link homologies via foams
David E. V. Rose, Paul Wedrich
We generalize results of Lee, Gornik and Wu on the structure of deformed colored sl(N) link homologies to the case of non-generic deformations. To this end, we use foam technology…
Symmetric webs, Jones-Wenzl recursions and -Howe duality
David E. V. Rose, Daniel Tubbenhauer
We define and study the category of symmetric -webs. This category is a combinatorial description of the category of all finite dimensional quantum $\mathfrak{sl}_…
The foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
Hoel Queffelec, David E. V. Rose
We give a purely combinatorial construction of colored link homology. The invariant takes values in a 2-category where 2-morphisms are given by foams, singular co…
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
Aaron D. Lauda, Hoel Queffelec, David E. V. Rose
We show that Khovanov homology (and its sl(3) variant) can be understood in the context of higher representation theory. Specifically, we show that the combinatorially defined foam…
A Note on the Grothendieck Group of an Additive Category
David E. V. Rose
There are two abelian groups which can naturally be associated to an additive category A: the split Grothendieck group of A and the triangulated Grothendieck group of the homotopy…
A Categorification of Quantum sl_3 Projectors and the sl_3 Reshetikhin-Turaev Invariant of Tangles
David E. V. Rose
We construct a categorification of the quantum sl_3 projectors, the sl_3 analog of the Jones-Wenzl projectors, as the stable limit of the complexes assigned to k-twist torus braids…