ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46, 82 Araki, Huzihiro, Science University of Tokyo, Japan Factor types of infrared representations of the XY-model Continuously many mutually disjoint positive energy primary representations of type III_{λ} for each λ are constructed for the XY-model at critical parameter values. The method is to make excitations at an infinite number of mutually disjoint energy intervals with a finite energy sum. For a fixed sequence of energy intervals, the choice of the intervals to be excited or not to be excited gives continuously many disjoint representations, while the choice of a mixed excited state for each excited intervals gives rise to different ITPF-I factors. This construction is first made for CAR system and then transferred to the spin algebra by an operator algebra techniques.