Webs of type Q

Brown, Gordon C.; Kujawa, Jonathan R.

doi:10.5802/alco.191

Webs of type Q

Brown, Gordon C.¹; Kujawa, Jonathan R.²

¹ Fort Worth, TX, USA
² Department of Mathematics University of Oklahoma Norman, OK 73019, USA

Algebraic Combinatorics, Volume 4 (2021) no. 6, pp. 1027-1072.

Abstract

Howe dualities lead to diagrammatic categories which describe the representations of Lie-type objects as a monoidal category (that is, via generators and relations). Applying this philosophy to the type Q Howe duality of Cheng–Wang and Sergeev, we introduce diagrammatic web supercategories of type Q via generators and relations and show they describe the full subcategory of supermodules for the Lie superalgebra of type Q given by the tensor products of supersymmetric tensor powers of the natural supermodule.

Received: 2018-03-19
Revised: 2021-06-30
Accepted: 2021-07-21
Published online: 2022-01-04

DOI: 10.5802/alco.191

Classification: 17B10, 18D10
Keywords: Monoidal supercategories, diagrammatic categories, web categories, Lie superalgebras.

Author's affiliations:

Brown, Gordon C. ¹; Kujawa, Jonathan R. ²

¹ Fort Worth, TX, USA
² Department of Mathematics University of Oklahoma Norman, OK 73019, USA

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Brown, Gordon C.; Kujawa, Jonathan R. Webs of type Q. Algebraic Combinatorics, Volume 4 (2021) no. 6, pp. 1027-1072. doi : 10.5802/alco.191. https://alco.centre-mersenne.org/articles/10.5802/alco.191/

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