Abstract
We study the infinite dimensional Grassmannian structure of 2D quantum gravity coupled to minimal conformal matters, and show that there exists a large symmetry, theW 1+∞ symmetry. Using this symmetry structure, we prove that the square root of the partition function, which is a τ function of thep-reduced KP hierarchy, satisfies the vacuum condition of theW 1+∞ algebra. We further show that this condition is reduced to the vacuum condition of theW p algebra when the redundant variables for thep-reduction are eliminated. This mechanism also gives a prescription for extracting theW p algebra from theW 1+∞ algebra.
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Communicated by H. Araki
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Fukuma, M., Kawai, H. & Nakayama, R. Infinite dimensional Grassmannian structure of two-dimensional quantum gravity. Commun.Math. Phys. 143, 371–403 (1992). https://doi.org/10.1007/BF02099014
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DOI: https://doi.org/10.1007/BF02099014