Lattices and Norton algebras of Johnson, Grassmann and Hamming graphs

Details Lattices and Norton algebras of Johnson, Grassmann and Hamming graphs Lattices and Norton algebras of Johnson, Grassmann and Hamming graphs

2012-04-09

arxiv.org/abs/1204.1947v1

Mathematics

Combinatorics

16 pages

Scientific paper

To each of the Johnson, Grassmann and Hamming graphs we associate a lattice and characterize the eigenspaces of the adjacency operator in terms of this lattice . We also show that each level of the lattice induces in a natural way a tight frame for each eigenspace. For the most important eigenspace we compute explicitly the constant associated to the tight frame. Using the lattice we also give a formula for the product of the Norton algebra attached to that eigenspace.

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