Connection between representations of nonstandard and standard Chebyshev oscillators

We continue consideration the generalized oscillator algebra related to Jacobi matrix which differs from ones for Chebyshev polynomials only by nonzero main diagonal, consisting from periodically repeated set of three numbers {i√(3), -i√(3), 0}. We show that representations of this algebra are connected with representations of three more simple generalized oscillator algebras, related to Chebyshev polynomials of second kind. This investigation is partially supported by RFBR grant No 09-01-00504-a.