ANOTHER LOOK AT THE DIFFERENTIAL OPERATORS ON QUANTUM MATRIX SPACES AND ITS APPLICATIONS Dedicated to Professor Kiyosato Okamoto on the occasion of sixtieth birthday

The present paper gives a new view point for the di erential operators with respect to the coordinates of the quantum matrix space. A special emphasis is put on an inductive construction of these di erential operators from the q-di erence operators de ned on each columns (resp. rows). This idea for understanding our operators provides us with two important applications: (1) a construction of the q-oscillator representations of the quantized enveloping algebra U q (sp 2m ) of symplectic Lie algebra sp 2m and an explicit description of their tensor powers; (2) a new de nition of a quantum analogue of hypergeometric equations of many variables.