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A Basis Theorem for the Degenerate Affine Oriented Brauer–Clifford Supercategory

Part of: Categories with structure Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  07 March 2019

Jonathan Brundan ,
Jonathan Comes  and
Jonathan Robert Kujawa
Jonathan Brundan
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222, USA Email: brundan@uoregon.edu
Jonathan Comes
Affiliation:
Department of Mathematics & Physical Sciences, The College of Idaho, Caldwell, Idaho 83605, United States Email: jonnycomes@gmail.com
Jonathan Robert Kujawa
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019-0315, United States Email: kujawa@math.ou.edu
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Abstract

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We introduce the oriented Brauer–Clifford and degenerate affine oriented Brauer–Clifford supercategories. These are diagrammatically defined monoidal supercategories that provide combinatorial models for certain natural monoidal supercategories of supermodules and endosuperfunctors, respectively, for the Lie superalgebras of type Q. Our main results are basis theorems for these diagram supercategories. We also discuss connections and applications to the representation theory of the Lie superalgebra of type Q.

Keywords

monoidal categorysupercategoryLie superalgebratype Q

MSC classification

Primary: 17B10: Representations, algebraic theory (weights)
Secondary: 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 5 , October 2019 , pp. 1061 - 1101
Copyright
© Canadian Mathematical Society 2019 

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