Conditional symmetries and the quantization of Bianchi type I vacuum cosmologies with and without cosmological constant. (English summary) Classical Quantum Gravity 19 (2002), no. 6, 1013–1025. In this paper the authors discuss the quantization of the most general Bianchi I model, with and without a cosmological constant. A consistent procedure for reduction of the number of degrees of freedom is developed and the resulting conditions, referred to as “conditional symmetries”, are imposed on the wavefunction of the quantum version of the classical integrals of motion. The vector fields arising by these integrals induce motions in the configuration space corresponding to the action of the automorphism group of the Bianchi model GL(3, R). The wavefunction of the resulting one-dimensional minisuperspace model, which depends on the determinant of the scale-factor matrix, is obtained and a measure for constructing the Hilbert space is proposed an
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