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Diagrammatics for real supergroups | Saima Samchuck-Schnarch
; Alistair Savage
; | Date: |
4 Jan 2023 | Abstract: | We introduce two families of diagrammatic monoidal supercategories. The first
family, depending on an associative superalgebra, generalizes the oriented
Brauer category. The second, depending on an involutive superalgebra,
generalizes the unoriented Brauer category. These two families of
supercategories admit natural superfunctors to supercategories of supermodules
over general linear supergroups and supergroups preserving superhermitian
forms, respectively. We show that these superfunctors are full when the
superalgebra is a central real division superalgebra. As a consequence, we
obtain first fundamental theorems of invariant theory for all real forms of the
general linear, orthosymplectic, periplectic, and isomeric supergroups. We also
deduce equivalences between monoidal supercategories of tensor supermodules
over the real forms of a complex supergroup. | Source: | arXiv, 2301.01414 | Services: | Forum | Review | PDF | Favorites |
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