Abstract
Starting from the covariant action for W 3 gravity we constructed in a previous paper [Phys. Lett. B274 (1992) 289], we discuss the BRST quantization of W 3 gravity. Taking the chiral gauge the BRST charge has a natural interpretation in terms of the quantum Drinfeld-Sokolov reduction for Sl(3, R ). Nilpotency of this charge leads to the KPZ formula for W 3. In the conformal gauge, where the covariant action reduces to a Toda action, the BRST charge is equivalent to the one recently constructed by Bershadsky et al. [Phys. Lett. B292 (1992) 35].
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