ON THE SPECTRUM OF DEHN TWISTS IN QUANTUM TEICHMÜLLER THEORY

Rinat Kashaev

Type: Preprint

Publication Date: 2001-04-01

Citations: 57

DOI: https://doi.org/10.1142/9789812810007_0004

Abstract

The operator realizing a Dehn twist in quantum Teichmuller theory is diagonalized and continuous spectrum is obtained. This result is in agreement with the expected spectrum of conformal weights in quantum Liouville theory at c>1. The completeness condition of the eigenvectors includes the integration measure which appeared in the representation theoretic approach to quantum Liouville theory by Ponsot and Teschner. The underlying quantum group structure is also revealed.

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