A quantum ergodic theorem for mapping class groups action on character variety

Abstract

We state a theorem relating the ergodicity of the action of a given subgroup of the mapping class group of a surface on the character variety, to the asymptotic of its invariant subspaces through the Witten-Reshetikhin-Turaev representations. As application we give an asymptotic result on the spin decomposition arising in TQFT.

References in corpus (3)

• Scarred eigenstates for quantum cat maps of minimal periods
• Irreducible factors of Weil representations and TQFT
• Geometric quantization and semi-classical limits of pairings of TQFT vectors