6J Symbols Duality Relations
Abstract
It is known that the Fourier transformation of the square of (6j) symbols has a simple expression in the case of su(2) and Uq(su(2)) when q is a root of unit. The aim of the present work is to unravel the algebraic structure behind these identities. We show that the double crossproduct construction H1 H2 of two Hopf algebras and the bicrossproduct construction H2* H1 are the Hopf algebras structures behind these identities by analysing different examples. We study the case where D= H1 H2 is equal to the group algebra of ISU(2), SL(2,C) and where D is a quantum double of a finite group, of SU(2) and of Uq(su(2)) when q is real.
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