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The image of the Burnside ring in the Representation ring for binary Platonic groups | | Simon Burton
; Hisham Sati
; Urs Schreiber
; | | Date: |
23 Dec 2018 | | Abstract: | We describe an efficient algorithm that computes, for any finite group G, the
linear span of its virtual permutation representations inside all its linear
representations, hence the image of the canonical morphism $eta$ from the
Burnside ring to the representation ring. We use this to determine the image
and cokernel of $eta$ for binary Platonic groups, hence for finite subgroups
of SU(2), over $k in {mathbb{Q}, mathbb{R}, mathbb{C}}$. We find
explicitly that for the three exceptional subgroups and for the first seven
binary dihedral subgroups, $eta$ surjects onto the sub-lattice of the real
representation ring spanned by the integer-valued characters. We conjecture
that, generally, this holds true for all the binary dihedral groups. | | Source: | arXiv, 1812.9679 | | Services: | Forum | Review | PDF | Favorites | |
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