Spectra of the Laplacian on the Cayley projective plane
type: Item
instance of: scholarly article
title: Spectra of the Laplacian on the Cayley projective plane
zbMATH Open document ID: 0906.58051
author: Katsuya Mashimo
published in: Tsukuba Journal of Mathematics
publication date: 1999-01-31T00:00:00Z
review text: Let \(\text{Ca}P^2 = F_4/\text{Spin}(9)\) denote the Cayley projective plane. The goal of the paper under review is to find the decomposition of the vector space of smooth \(p\)-forms on \(\text{Ca}P^2\) into the direct sum of irreducible \(F_4\)-submodules and to find the corresponding eigenvalues of the Laplacian. This problem is completely solved for \(0\leq p\leq 5\), using Frobenius reciprocity and the results of J. Lepovsky about the branching law of the pair \((F_4, \text{Spin}(9))\).
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 58A10
zbMATH DE Number: 1102897
zbMATH Keywords: Cayley projective plane
zbMATH Keywords: Frobenius reciprocity
zbMATH Keywords: branching law
zbMATH Keywords: Laplacian
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496163248
OpenAlex ID: W149726014
DOI: 10.21099/TKBJM/1496163248
description: scientific article; zbMATH DE number 1102897