#What is lambda5?? lambda1.append([(4,), (4,), (0,), (0,)]) lambda5.append(expand("[(6,)^2/(4,)^2/(2,)^2/(0,)^2]")) #What is the spin here? lambda1.append([(5,), (5,)]) lambda5.append(expand("[(8,)^2/(4,)^2/(0,)^4]")) for i in range(1,len(lambda1)): lambda2.append(wedge2(lambda1[i])) #print(dimChecker(lambda2[i])) orderList2=order(2) L=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] for i in range(1,len(lambda1)): L[i]=[] L[i]=L[i]+concat([(0,)],lambda2[i]) L[i]=L[i]+[(2,0)] L[i]=L[i]+concat([(1,)],lambda5[i]) x=checker(L[i],basisA12,orderList2) # print("///////////////////////////////") # print(i) # print(x) basisA12.append(L[i]) basisA12Lambda1.append(lambda1[i]) checker(L[i],basisA12,orderList2) # if dimChecker(L[i])!=133: # print("////////////////////////////////////")
a=expand("[(2,0,0,0,0,0,0,0)/(0,2,0,0,0,0,0,0)/(0,0,2,0,0,0,0,0)/(0,0,0,2,0,0,0,0)/(0,0,0,0,2,0,0,0)/(0,0,0,0,0,2,0,0)/(0,0,0,0,0,0,2,0)/(0,0,0,0,0,0,0,2)/(1,1,1,1,0,0,0,0)/(1,1,0,0,1,1,0,0)/(1,1,0,0,0,0,1,1)/(1,0,1,0,1,0,0,1)/(1,0,1,0,0,1,1,0)/(1,0,0,1,1,0,1,0)/(1,0,0,1,0,1,0,1)/(0,0,1,1,1,1,0,0)/(0,0,1,1,0,0,1,1)/(0,0,0,0,1,1,1,1)/(0,1,1,0,1,0,0,1)/(0,1,1,0,0,1,1,0)/(0,1,0,1,1,0,1,0)/(0,1,0,1,0,1,0,1)]") print("A18") print(dimChecker(a)) print(latex(a)) basisA18=[[0]] basisA18.append(a) ############################################################### ############################################################### ###########A17 ############################################################### ############################################################### a=[0,0,0,0,0,00,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,00,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,00,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,00,0,0,0,0,0,0,0,0,0,0] orderList = order(7) basisA17=[[0]] #We make the basis from basis of A18 a[0]=diagA1(basisA18[1],1,2) a[1]=removeA1(basisA18[1],1) basisA17.append(a[0]) basisA17.append(a[1]) a[0]=expand("[(2,0,0,0,0,0,0)/(0,2,0,0,0,0,0)^2/(0,0,2,0,0,0,0)/(0,0,0,2,0,0,0)/(0,0,0,0,2,0,0)/(0,0,0,0,0,2,0)/(0,0,0,0,0,0,2)/(1,2,1,0,0,0,0)/(1,0,1,0,0,0,0)/(1,1,0,1,1,0,0)/(1,1,0,0,0,1,1)/(1,1,0,1,0,0,1)/$(1,1,0,0,1,1,0)/(1,0,1,1,0,1,0)/(1,0,1,0,1,0,1)/(0,1,1,1,1,0,0)/(0,1,1,0,0,1,1)/(0,0,0,1,1,1,1)/(0,2,0,1,0,0,1)/(0,0,0,1,0,0,1)/(0,2,0,0,1,1,0)/(0,0,0,0,1,1,0)/(0,1,1,1,0,1,0)/(0,1,1,0,1,0,1)]") print("First one in notes corresponds to 1rst one from A18?") print(checker(a[0], basisA17,orderList )) a[1]=expand("[(2,0,0,0,0,0,0,0)/(0,2,0,0,0,0,0,0)/(0,0,2,0,0,0,0,0)/(0,0,0,2,0,0,0,0)/(0,0,0,0,2,0,0,0)/(0,0,0,0,0,2,0,0)/(0,0,0,0,0,0,2,0)/(0,0,0,0,0,0,0,2)/(1,1,1,1,0,0,0,0)/(1,1,0,0,1,1,0,0)/(1,1,0,0,0,0,1,1)/(1,0,1,0,1,0,0,1)/(1,0,1,0,0,1,1,0)/(1,0,0,1,1,0,1,0)/(1,0,0,1,0,1,0,1)/(0,0,1,1,1,1,0,0)/(0,0,1,1,0,0,1,1)/(0,0,0,0,1,1,1,1)/(0,1,1,0,1,0,0,1)/(0,1,1,0,0,1,1,0)/(0,1,0,1,1,0,1,0)/(0,1,0,1,0,1,0,1)]")
basisA13.append(expand("[(2,0,0)/(0,2,0)/(0,0,2)/(1,1,1)^2/(1,1,0)^2/(1,0,1)^2/(0,1,1)^2/(1,0,0)^4/ (0,1,0)^4/(0,0,1)^4/(0,0,0)^5]")) basisA13.append(expand("[(0,6,0)/(1,4,1)/(0,4,0)/(1,3,0)^2/(0,3,1)^2/(2,0,0)/(0,2,0)/(0,0,2)/ (1,0,1)/(0,0,0)]")) basisA13.append(expand("[(1,1,1)^4/(2,2,0)/(2,0,2)/(0,2,2)/(0,2,0)^2/(0,0,2)^2/(2,0,0)^2/(0,0,0)]")) basisA13.append(expand("[(2,2,2)^2/(4,0,0)/(0,4,0)/(0,0,4)/(2,0,0)/(0,2,0)/(0,0,2)]")) for i in range(1,len(basisA13)): print(dimChecker(basisA13[i])) order3=order(3) for i in range(1,len(lam)): x=wedge2(lam[i]) n=classifyIncomplete(x,basisA13,order3) p=str(i) + " & " +latex(lam[i])+" & "+ latex(x)+ " & "+str(n[1])+"\\\\ \\hline" print(p) print("//////////////////////////////") print("A12") print("/////////////////////////////") lam2 = [0] lam2.append([(1, 1), (1, 1), (0, 0), (0, 0)]) lam2.append([(1, 1), (1, 0), (1, 0), (0, 0), (0, 0)])
basis.append(a) #51&$(2,1)^2$&$ Maybe case 81?? a[1] = expand("[(2,0,0)/(0,2,0)/(0,0,2)/(0,2,2)^3/(0,4,0)^3/(0,4,2)/(0,0,0)^3]") basis.append(a[1]) #52&$(5,1)^2 82?? a[1] = expand("[(0,10,0)/(0,8,2)/(0,4,2)/(0,6,0)/(1,8,1)/(1,4,1)/(1,0,3)/(2,0,0)/(0,2,0)/(0,0,2)]") basis.append(a[1]) #53&$(2,2)/(0,0)^3 82?? a[1] = expand("[(1,3,1)^2/(1,1,3)^2/(2,0,0)/(0,4,2)/(0,2,4)/(0,2,0)/(0,0,2)/(0,2,2)^3/(0,0,0)^3]") print("This is the last case") print(dimChecker(a[1])) orderList3=order(3) print(checker(a[1],basis,orderList3)) basis.append(a[1]) options=[] #case 1 (2,1,1) a=expand("[ (4,2,0)/(4,0,2)/(2,2,2)/(2,0,0)/(0,2,0)/ (0,0,2)/(0,0,0)^3/(2,1,2)^2/(4,1,0)^2/(0,3,0)^2 ]") basis.append(a)
#VD8(lambda1) has dim 12 d=16 L=[] #List of all possible weights for i in range(0,d-1): if i%2==0: L.append([(i,0,0,0,0)]) else : temp=[(i,0,0,0,0),(i,0,0,0,0)] tempdim=dimChecker(temp) if tempdim<=d: L.append(temp) o=order(5) for i in range(0,len(L)): for j in range(0,len(o)): temp=perm(o[j],L[i]) if temp not in L: L.append(temp) Ladd = [[(1,1,0,0,0)],[(2,2,0,0,0)],[(1,3,0,0,0)],[(1,1,2,0,0)]] for i in range(0,len(Ladd)): for j in range(0,len(o)): temp=perm(o[j],Ladd[i]) if temp not in Ladd: Ladd.append(temp) L= L+Ladd