Co- and Contra-Variant Tensors of a General Rankin Quantum Matrix Algebrassuq(2) Expressedby Creation-Annihilation Operators. I

Abstract

Quantum matrix algebras s u q (2) are formulated in terms of the co-variant and the contra-variant spinors ( a + , b + ), ( a , b ) subject to linear transformations of S U q (2), a ′+ = a + x + b + v , b ′+ = a + u + b + y , a ′ = a x * + b v * and b ′ = a u * + b y * , where x , u , v , y with and without * are non-commutative objects. Commutation relations, which are quadratic in spinor components, are determined with the following conditions: (i) invariance under the linear transformations of S U q (2) and (ii) uniqueness of scalar and co-variant vectors made of spinor components. Commutation relations for A + ( j ′ m ′ ; a + , b + ) and A + j ′′ m ′′ ; e + , f + ), where A + ( j ′′ m ′′ ; e + , f + ) is the m ′′ -component of rank-j ′′ co-variant tensor written as polynomials in components of spinor ( e + , f + ), give Zamolodchikov-Zamolodchikov equations with (2 j ′ +1)×(2 j ′′ +1) universal R matrix elements of s u q (2). The (2 j +1)-dimensional matrix { d m k j ( a + , b + , e + , f + )} is pres...