On the spectrum of Dehn twists in quantum Teichmuller theory

Details On the spectrum of Dehn twists in quantum Teichmuller theory On the spectrum of Dehn twists in quantum Teichmuller theory

2000-08-18

arxiv.org/abs/math/0008148v1

Mathematics

Quantum Algebra

13 pages,8 figures,LaTeX2e

Scientific paper

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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