- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:39
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
4
2013
1
A diagrammatic categorification of the q-Schur algebra
Marco
Mackaay
Universidade do Algarve, FARO, PORTUGAL
Marko
Stošić
Instituto Superior Técnico, LISBOA, PORTUGAL
Pedro
Vaz
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
Categorification, quantum groups, quantum $\mathfrak{gl}_n$, q-Schur algebra, Soergel category
In this paper we categorify the q-Schur algebra $\mathbf{S}_q(n,d)$ as a quotient of Khovanov and Lauda’s diagrammatic 2-category $\mathcal{U}(\mathfrak{sl}_n)$ [16]. We also show that our 2-category contains Soergel’s [33] monoidal category of bimodules of type $A$, which categorifies the Hecke algebra $H_q(d)$, as a full sub-2-category if $d\leq n$. For the latter result we use Elias and Khovanov’s diagrammatic presentation of Soergel’s monoidal category of type $A$; see [8].
Quantum theory
Algebraic geometry
Associative rings and algebras
Nonassociative rings and algebras
1
75
10.4171/QT/34
http://www.ems-ph.org/doi/10.4171/QT/34