Quantum integrable system with two color components in two dimensions

The Davey-Stewartson I (DSI) system [Proc. R. Sec. London, Ser. A 338, 101 (1974)] is an integrable model in two dimensions. A quantum DS1 system with two color components in two dimensions has been reformulated. This two-dim ensional problem has been reduced to two one-dimensional many-body problems with two color components. The solutions to the two-dimensional problem un der consideration can be constructed from the resulting problem in one dime nsions. For the latter problem with delta-function interactions and solutio n by the Bethe ansatz, we introduce symmetrical and antisymmetrical Young o perators of the permutation group and obtain the exact solutions for the qu antum DS1 system.