G=group[g,i]G=so[2]G=o[2]G=so[3]G=o[3]G=su[2]G=su[4]G=dih[N](N: even)G=dih[N](N: odd)G=dic[N]G=pGroup[G1,G2]
All labels of irreps are defined as follows:
All irreps are labeled by rep[n] (n=1,2,...,g[ncg]).
rep[n] corresponds to n-th irrep in Irr(SmallGroup(g,i)) in GAP.
The character table can be accessed by G[ct] and n-th row is the character of rep[n].
G[id] is rep[1].
All irreps are labeled by v[x] (x is a real number).
Let G is generated by s.
v[x] is the 1-dimensional representation in which s is represented by {{x}}.
G[id] is v[0] and the standard vector representation is v[1].
All irreps are labeled by i[1], i[-1] or v[n] (n=1,2,...).
Let G is generated by s={{0,-1}, {1,0} and t={{1,0}, {0,-1}}.
i[\pm 1] is the 1-dimensional representation in which t is represented by {{\pm 1}}.
v[n] is the 2-dimensional representation in which s is represented by {{0,-n}, {n,0}}.
G[id] is i[1] and the standard vector representation is v[1].
All irreps are labeled by v[n] (n=0,1,2,...).
v[n] is the spin-n representation, which dimension is 2*n+1.
G[id] is v[0] and the standard vector representation is v[1].
All irreps are labeled by v[n,\pm 1] (n=0,1,2,...).
v[n,\pm 1] is the spin-n representation which represents the inversion diag(-1,-1,-1) by \pm 1.
G[id] is v[0,1] and the standard vector representation is v[1,-1].
All irreps are labeled by v[n] (n=0,1/2,1,3/2,...).
v[n] is the spin-n representation, which dimension is 2*n+1.
G[id] is v[0] and the standard vector representation is v[1].
All irreps are labeled by v[n, m, l] (n,m,l=0,1,2,... and n>=m>=l).
An irrep v[n, m, l] corresponds to a young tableaux
which has n boxes in first row, m boxed in second row and l boxed in third row.
G[id] is v[0, 0, 0] and the standard vector representation is v[1, 0, 0].
The adjoint representation is v[2, 1, 1].
All irreps are labeled by i[\pm 1,\pm 1] and v[n] (n=1,2,...,N/2-1).
Let G is generated by s={{q,0}, {0,1/q}} (q=exp(2Pi/N)) and t (reflection by y=x).
i[p,q] (p,q=\pm 1) represents s by {{q}} and t by {{p}}.
v[n] represents s by s^n and t as-is.
G[id] is i[1,1] and the standard vector representation is v[1].
All irreps are labeled by i[\pm 1] and v[n] (n=1,2,...,(N-1)/2).
Let G is generated by s={{q,0}, {0,1/q}} (q=exp(2Pi/N)) and t (reflection by y=x).
i[\pm 1] represents s by {{1}} and t by {{\pm 1}}.
v[n] represents s by s^n and t as-is.
G[id] is i[1] and the standard vector representation is v[1].
All irreps are labeled by i[\pm 1,\pm 1] and v[n] (n=1,2,...,N-1).
Let G is generated by s={{q,0}, {0,1/q}} (q=exp(Pi/N)) and t (Pi/2 rotation).
i[p,q] (p,q=\pm 1) represents s by {{p}} and t by {{q}} or {{q I}}.
v[n] represents s by s^n and t by {{0,(-1)^n},{1,0}}.
G[id] is i[1,1] and the standard vector representation is v[1].
All irreps are labeled by rep[r1,r2]
(r1 is a irrep of G1 and r2 is a irrep of G2).
rep[r1,r2] is a external tensor product of r1 and r2.
G[id] is rep[G1[id],G2[id]].