TY - JOUR
AB - For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of
arbitrary rank we determine the location of certain Ruelle-Taylor resonances
for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate
counting function for the Ruelle-Taylor resonances and establish a spectral gap
which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is
achieved by proving a quantum-classical correspondence, i.e. a
1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant
states and joint eigenfunctions of the algebra of invariant differential
operators on $G/K$.
AU - Hilgert, Joachim
AU - Weich, Tobias
AU - Wolf, Lasse Lennart
ID - 31190
IS - 10
JF - Analysis & PDE
TI - Higher rank quantum-classical correspondence
VL - 16
ER -