Lattices, frames and Norton algebras of dual polar graphs

FERNANDO LEVSTEIN; CAROLINA MALDONADO; DANIEL PENAZZI

New developments in Lie Theory and its applications

AMS

Lugar: Povidence; Año: 2011; p. 1 - 16

To a dual polar graph (X;E) we associate a graded lattice, map the lattice onto L2(X) and characterize the eigenspaces of the adjacency op- erator ∆ in L2(X) in terms of this map, each one corresponding to the levels of the lattice. The map also induces in a natural way a tight frame on each eigenspace of ∆, and we find the constants associated to each tight frame. As an application we give a formula for the product of the Norton algebra of the eigenspace associated to the second largest eigenvalue of ∆.