Lattices, frames and Norton algebras of dual polar graphs.

F.LEVSTEIN; C. MALDONADO; D. PENAZZI

CONTEMPORARY MATHEMATICS

American Mathematical Society

Lugar: Providence; Año: 2010

0271-4132

Abstract. To a dual polar graph Gamma=(X;E) we associate a graded lattice, mapthe lattice onto L^2(X) and characterize the eigenspaces of the adjacency operator Delta in L2(X) in terms of this map, each one corresponding to the levelsof the lattice. The map also induces in a natural way a tight frame on eacheigenspace of Delta, and we find the constants associated to each tight frame. Asan application we give a formula for the product of the Norton algebra of theeigenspace associated to the second largest eigenvalue of Delta.