TL;DR
This paper explores the structure of the representation theory of Z2-graded coalgebras, connecting it to Fourier analysis on supergroups and providing explicit examples with super linear groups.
Contribution
It generalizes the representation theory of super coalgebras and illustrates its application to supergroups, including detailed examples with general linear supergroups.
Findings
Representation theory structure of Z2-graded coalgebras analyzed
Connections established with Fourier analysis on supergroups
Explicit examples with general linear supergroups provided
Abstract
The general structure of the representation theory of a -graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear supergroups serve as an explicit illustration and the simplest example is carried out in detail.
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