Determinant Formulae of Quasi-Finite Representation of W1+∞ Algebra at Lower Levels
H. Awata, M. Fukuma, Y. Matsuo, S. Odake
Abstract
We calculate the Kac determinant for the quasi-finite representation of algebra up to level 8. It vanishes only when the central charge is integer. We give an algebraic construction of null states and propose the character formulae. The character of the Verma module is related to free fields in three dimensions which has rather exotic modular properties.
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