THE QUANTUM SYMMETRIES AND ANTISYMMETRIES OF MATRICES AND THE HIGH-DIMENSIONAL REALIZATIONS OF THE QUANTUM GROUPS GL(LAMBDA-QIJ)(N) AND GL(LAMBDA-QIJ)(N)XGL(LAMBDA-QIJ)(N)
Zz. Zhong, THE QUANTUM SYMMETRIES AND ANTISYMMETRIES OF MATRICES AND THE HIGH-DIMENSIONAL REALIZATIONS OF THE QUANTUM GROUPS GL(LAMBDA-QIJ)(N) AND GL(LAMBDA-QIJ)(N)XGL(LAMBDA-QIJ)(N), Modern physics letters A, 11(25), 1996, pp. 2047-2052
In this letter, the (pij)-symmetry and the (qij)-antisymmetry of matri
ces are defined, it is proved that the above two quantum symmetries ar
e invariant under a GL(lambda iqij)(N)-involution transformation. By t
hese quantum symmetries, a (1.2 N-2(N-1))-dimensional and a (1/2N(2)(N
-1))-dimensional hyperspaces are constructed, and on them the quantum
groups GL(lambda iqij)(N) and GL(lambda iqij)(N) x GL(lambda iqij) (N)
are realized respectively.