559 research outputs found
A basis theorem for the degenerate affine oriented Brauer-Clifford supercategory
We introduce the oriented Brauer-Clifford and degenerate affine oriented
Brauer-Clifford supercategories. These are diagrammatically defined monoidal
supercategories which 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.Comment: 37 pages, many figures. Version 3 replaces the partial results from
the previous versions with a proof by the first author of a basis theorem for
cyclotomic quotients at all levels. Various other minor corrections and
revisions were mad
Webs of Type P
This paper introduces type P web supercategories. They are defined as
diagrammatic monoidal -linear supercategories via generators and relations.
We study the structure of these categories and provide diagrammatic bases for
their morphism spaces. We also prove these supercategories provide
combinatorial models for the monoidal supercategory generated by the symmetric
powers of the natural module and their duals for the Lie superalgebra of type
P.Comment: Final version. Compared to the first version, there are no
substantive changes to the mathematics, but numerous changes to exposition in
response to referee suggestions. Updated authors' affiliation
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