Daniel Tubbenhauer

THE sl3-WEB ALGEBRA

In this paper we use Kuperbergs sl3-webs and Khovanovs sl3-foams to define a new algebra K S , which we call the sl3-web algebra. It is the sl3 analogue of Khovanovs arc algebra. We prove that K S is a graded symmetric Frobenius algebra. Furthermore, we categorify an instance of q-skew Howe duality, which allows us to prove that K S is Morita equivalent to a cer- tain cyclotomic KLR-algebra of level 3. This allows us to determine the split Grothendieck group K ⊕ 0 (W S )Q(q), to show that its center is isomorphic to the cohomology ring of a certain Spaltenstein variety, and to prove that K S is a graded cellular algebra.

Super q-Howe duality and web categories

We use super

Symmetric Webs, Jones–Wenzl Recursions, and q-Howe Duality

q

Cellular structures using TEXTBACKSLASHmathboldTEXTBACKSLASHUq-tilting modules

-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of

DIAGRAM CATEGORIES FOR Uq-TILTING MODULES AT ROOTS OF UNITY

\mathfrak{gl}_N

SEMISIMPLICITY OF HECKE AND (WALLED) BRAUER ALGEBRAS

-modules (and, more generally,

Functoriality of colored link homologies

\mathfrak{gl}_{N|M}

The Blanchet-Khovanov algebras

-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.

Webs and

We define and study the category of symmetric

q

\mathfrak{sl}_2