A diagrammatic categorification of the q-Schur algebra

By Marco Mackaay, Marko Stosic, Pedro Vaz. 2010

55 citations recorded by the source corpus.

In this paper we categorify the q-Schur algebra Sq(n,d) as a quotient of Khovanov and Lauda’s diagrammatic 2-category Uq(sln)[16]. We also show that our 2-category contains Soergel’s [33] monoidal category of bimodules of type A, which categorifies the Hecke algebra Hq(d), as a full sub-2-category if d is smaller or equal to n. For the latter result we use Elias and Khovanov’s diagrammatic presentation of Soergel’s monoidal category of type A (see [8]).

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0d906b5de1568de3156f602c657eb31b4a12fa3d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. David E. V. Rose
2. Hoel Queffelec
3. Aaron D. Lauda
4. Mikhail Khovanov
5. Stephen Lack
6. Ben Webster
7. A. Henriques
8. J. Elgueta

In Discrete Mathematics and Combinatorics

1. David E. V. Rose
2. Hoel Queffelec
3. Aaron D. Lauda

In Geometry and Topology

1. David E. V. Rose
2. Hoel Queffelec
3. Aaron D. Lauda
4. Paul Wedrich
5. Sabin Cautis
6. Mikhail Khovanov
7. Ben Webster
8. Jonathan Brundan

Citations in the corpus

• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, background): “They allow us to 2One can define the 2-category so that degree zero bubbles are multiplication by arbitrary scalars at the cost of modifying some of the other relations, see for example [45, 52].”