Examples Worksheet #2:Large Examples: 3-fold SU(3), 2-fold SU(4) Special Note: It does not matter whether this worksheet or the TabProcs worksheet is opened first. After opening one of these, ensure that the Kernal mode is set to shared before opening the second. Also ensure that the Procedures have been loaded into memory by clicking on any of the red code (in that Worksheet) and pressing enter.

The Irrep and Tensor Product is entered as follows: Irrep := [4,3,2,0,0,0]: Tensors := [[2,1,0],[2,1,0],[2,1,0]]: Map the Highest Weight Vector in Terse Mode MapHW( Terse ); Apply the First Casimir Operator to Couple 1 & 2 lambda1, P1 := Casimir[first]( [[1,2],[2,2],[2,1]] ): lambda1; Apply a commuting Casimir Operator to more fully specify coupling scheme lambda1, P1 := Casimir[additional]( [[[1,3],[3,3],[3,1]], [[2,3],[3,3],[3,2]]] ): lambda1; Apply a different Casimir Operator to Couple 2 & 3 lambda2, P2 := Casimir[first]( [[2,3],[3,3],[3,2]] ): lambda2; Apply a commuting Casimir Operator to more fully specify coupling scheme lambda2, P2 := Casimir[additional]( [[[2,1],[1,1],[1,2]], [[3,1],[1,1],[1,3]]] ): lambda2; Compute Racah Coefficients Racah(P1, P2);

Choose another Irrep and Tensor Product Irrep := [4,3,3,2,0,0,0,0,0]; Tensors := [[2,1,1,0], [2,1,1,0], [2,1,1,0]]; Map the Hightest Weight Vector in Verbose Mode ( ~20 minutes on average machine ) MapHW(); Export_MapHW("3f_su4"); Apply a 4th degree Casimir Operator coupling 1 & 2 (~4 hrs) lambda1, P1 := Casimir[first]( [[1,2],[2,2],[2,2],[2,1]] ): lambda1; Another to break the degeneracy (~8 hrs) lambda1, P1 := Casimir:-additional( [[[1,3],[3,3],[3,3],[3,1]], [[2,3],[3,3],[3,3],[3,2]]] ): lambda1; ExportMatrix("3f_su4_lambda1.txt", lambda1); ExportMatrix("3f_su4_P1.txt", P1); Apply a new scheme, coupling 1 & 3 (~4 hrs) lambda2, P2 := Casimir[first]( [[1,3],[3,3],[3,3],[3,1]] ): lambda2; Another operator to break degeneracy (~8 hrs) lambda2, P2 := Casimir:-additional( [[[1,2],[2,2],[2,2],[2,1]], [[3,2],[2,2],[2,2],[2,3]]] ): lambda2; ExportMatrix("3f_su4_lambda2.txt", lambda2); ExportMatrix("3f_su4_P2.txt", P2); Compute the Racah Coefficients betweent the coupling schemes (~1 hr) R := Racah( P1, P2 ); Export_Racah("3f_su4");