Supercharacter theories for algebra group extensions
A.N.Panov
TL;DR
This paper develops supercharacter theories for certain algebra group extensions, including semidirect products and parabolic subgroups of GL(n), generalizing existing theories and classifying supercharacters and superclasses.
Contribution
It introduces new supercharacter theories for algebra group extensions and classifies supercharacters and superclasses for parabolic subgroups of GL(n).
Findings
Supercharacter theories for algebra group extensions are constructed.
Supercharacter theories for parabolic subgroups of GL(n) are classified.
Theories for algebra groups match those of Diaconis and Isaaks.
Abstract
We construct a few supercharacter theories for finite semidirect products with the normal subgroup of algebra group type. In the case of algebra groups, these supercharacter theories coincide with the one of P.Diaconis and I.M.Isaaks. For the parabolic subgroups of , the supercharacters and superclasses are classified.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry