Quantum Algebra UQ(3): Recent Results

In Refs. 1 and 2 the combined method was suggested to calculate the Clebsch-Gordan coefficients (CGC) for the quantum algebra SUq(3). It was used to find the isofactors (1) % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacqGH8aapcaGGOaGaeq4UdWMaeqiVd0MaaiykaiabgEna0kaacIca % cqaH7oaBpaWaaSbaaSqaa8qacaaIYaaapaqabaGcpeGaeqiVd02dam % aaBaaaleaapeGaaGOmaaWdaeqaaOWdbiaacMcacaGG8bGaaiiFaiaa % cIcacuaH7oaBgaqbaiqbeY7aTzaafaGaaiykaiabg6da+8aadaqhaa % WcbaWdbiaadghaa8aabaWdbiabeg8aYbaaaaa!5019! $$ _q^\rho $$ , of the CGCs for the tensor product (2) % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaGGOaGaeq4UdWMaeqiVd0MaaiykaiabgEna0kaacIcacqaH7oaB % paWaaSbaaSqaa8qacaaIYaaapaqabaGcpeGaeqiVd02damaaBaaale % aapeGaaGOmaaWdaeqaaOWdbiaacMcacqGH9aqpdaaeqbWdaeaapeGa % eqyVd42damaaBaaaleaapeGafq4UdWMbauaacuaH8oqBgaqbaaWdae % qaaaqaa8qacuaH7oaBgaqbaiaacYcacuaH8oqBgaqbaaqab0Gaeyye % IuoakiaacIcacuaH7oaBgaqbaiqbeY7aTzaafaGaaiykaiaacYcaaa % a!56B9! $$ (\lambda \mu ) \times ({\lambda _2}{\mu _2}) = \sum\limits_{\lambda ',\mu '} {{\nu _{\lambda '\mu '}}} (\lambda '\mu '),$$ of two irreps of the SUq(3)algebra. In (1) ρis a repetition index which distinguishes the multiple irreps (λ′μ′) appearing in the expansion (2) with the multiplicity νλ′μ′, i. e.ρ = 1,2,..., νλ′μ′. In [1] the multiplicity free tensor products with (λ2μ2) = (10), (01), (20), (02) were considered.