Categorifications of the extended affine Hecke algebra and the affine q-Schur algebra S(n,r) for 2 < r < n

Anne-Laure Thiel; Marco Mackaay

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Categorifications of the extended affine Hecke algebra and the affine q-Schur algebra S(n,r) for 2 < r < n

Marco Mackaay, Anne-Laure Thiel

Quantum Algebra · Submitted 13 Feb 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We categorify the extended affine Hecke algebra and the affine quantum Schur algebra S(n,r) for 2 < r < n, using Elias-Khovanov and Khovanov-Lauda type diagrams.

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arXiv ID1302.3102 (version 3)

Pith IDZQOOMAB5, Pith's permanent record of this paper and its review

CitationAnne-Laure Thiel, Marco Mackaay. "Categorifications of the extended affine Hecke algebra and the affine q-Schur algebra S(n,r) for 2 < r < n." arXiv:1302.3102 (2013). https://pith.science/paper/ZQOOMAB5

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We categorify the extended affine Hecke algebra and the affine quantum Schur algebra S(n,r) for 2 < r < n, using Elias-Khovanov and Khovanov-Lauda type diagrams. We also define the affine analogue of the Elias-Khovanov and the Khovanov-Lauda 2-representations of these categorifications into an extension of the 2-category of affine (singular) Soergel bimodules.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We categorify the extended affine Hecke algebra and the affine quantum Schur algebra S(n,r) for 2 < r < n, using Elias-Khovanov and Khovanov-Lauda type diagrams.	contribution 1.00	0.95	0.78	asserted 1.00
s1	We also define the affine analogue of the Elias-Khovanov and the Khovanov-Lauda 2-representations of these categorifications into an extension of the 2-category of affine (singular) Soergel bimodules.	contribution 0.99	0.94	0.17	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We categorify the extended affine Hecke algebra and the affine quantum Schur algebra S(n,r) for 2 < r < n, using Elias-Khovanov and Khovanov-Lauda type diagrams. We also define the affine analogue of the Elias-Khovanov and the Khovanov-Lauda 2-representations of these categorifications into an extension of the 2-category of affine (singular) Soergel bimodules.

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3 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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A very useful tool for this is provided by [ref] .

Skein Modules from Skew Howe Duality and Affine Extensions · … to better recover it? · 1.00

Cites it as background 2 papers

Note that a recent paper by Mackaay and Thiel [ref] presents a categorification of affine $q$-Schur algebras.

Skein Modules from Skew Howe Duality and Affine Extensions · Affine extensions · 0.92
Fiat $2$-categories also appear, sometimes in disguise, in [ref] and many other papers.

Isotypic faithful $2$-representations of $\mathcal{J}$-simple fiat $2$-categories · Introduction · 0.81

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