Symmetry of Mather singularities | Thom polynomial portal

Symmetry data of Mather singularities.

The Poincare-series presented here satisfy the spectral sequence test.

1: name
2: source weights of genotype (for a torus dominating the maximal torus)
3: target weights of genotype with minimal l
4: unfolding space weights for minimal l
5: weights of local algebra
6: Poincaré series for minimal l

SymmetryData:=[

[A0,[],[],[],[],1],

[A1,[a[1]],[2*a[1]],[],[a[1]],1/(1-q)],

[A2,[a[1]],[3*a[1]],[2*a[1]],[a[1],2*a[1]],1/(1-q)],

[A3,[a[1]],[4*a[1]],[2*a[1],3*a[1]],[a[1],2*a[1],3*a[1]],1/(1-q)],

[A4,[a[1]],[5*a[1]],[2*a[1],3*a[1],4*a[1]],[a[1],2*a[1],3*a[1],4*a[1]],1/(1-q)],

[A5,[a[1]],[6*a[1]],[2*a[1],3*a[1],4*a[1],5*a[1]],[a[1],2*a[1],3*a[1],4*a[1],5*a[1]],1/(1-q)],

[A6,[a[1]],[7*a[1]],[2*a[1],3*a[1],4*a[1],5*a[1],6*a[1]],[a[1],2*a[1],3*a[1],4*a[1],5*a[1],6*a[1]],1/(1-q)],

[A7,[a[1]],[8*a[1]],[2*a[1],3*a[1],4*a[1],5*a[1],6*a[1],7*a[1]],[a[1],2*a[1],3*a[1],4*a[1],5*a[1],6*a[1],7*a[1]],1/(1-q)],

[A8,[a[1]],[9*a[1]],[2*a[1],3*a[1],4*a[1],5*a[1],6*a[1],7*a[1],8*a[1]], [a[1],2*a[1],3*a[1],4*a[1],5*a[1],6*a[1],7*a[1],8*a[1]],1/(1-q)],

[A9,[a[1]],[10*a[1]],[2*a[1],3*a[1],4*a[1],5*a[1],6*a[1],7*a[1],8*a[1],9*a[1]],[a[1],2*a[1],3*a[1],4*a[1],5*a[1],6*a[1],7*a[1],8*a[1],9*a[1]],1/(1-q)],

[I22,[a[1],a[2]],[2*a[1],2*a[2]],[2*a[1]-a[2],2*a[2]-a[1]],[a[1],a[2],a[1]+a[2]],1/((1-q)*(1-q^2))],

[I23,[3*a[1],2*a[1]],[5*a[1],6*a[1]],[3*a[1],4*a[1],2*a[1]],[3*a[1],2*a[1],4*a[1],6*a[1]],1/(1-q)],

[I24,[4*a[1],2*a[1]],[6*a[1],8*a[1]],[4*a[1],6*a[1],4*a[1],2*a[1]],[4*a[1],2*a[1],4*a[1],6*a[1],8*a[1]],1/(1-q)],

[I25,[5*a[1],2*a[1]],[7*a[1],10*a[1]],[5*a[1],8*a[1],6*a[1],4*a[1],2*a[1]],[5*a[1],2*a[1],4*a[1],6*a[1],8*a[1],10*a[1]],1/(1-q)],

[I26,[6*a[1],2*a[1]],[8*a[1],12*a[1]],[6*a[1],10*a[1],8*a[1],6*a[1],4*a[1],2*a[1]],[6*a[1],2*a[1],4*a[1],6*a[1],8*a[1],10*a[1],12*a[1]],1/(1-q)],

[I27,[7*a[1],2*a[1]],[9*a[1],14*a[1]],[7*a[1],12*a[1],10*a[1],8*a[1],6*a[1],4*a[1],2*a[1]],[7*a[1],2*a[1],4*a[1],6*a[1],8*a[1],10*a[1],12*a[1]],1/(1-q)],

[I33,[3*a[1],3*a[1]],[6*a[1],9*a[1]],[6*a[1],3*a[1],6*a[1],3*a[1]],[3*a[1],6*a[1],3*a[1],6*a[1],9*a[1]],1/(1-q)],

[I34,[4*a[1],3*a[1]],[7*a[1],12*a[1]],[8*a[1],4*a[1],9*a[1],6*a[1],3*a[1]],[4*a[1],8*a[1],12*a[1],3*a[1],6*a[1],9*a[1]],1/(1-q)],

[I35,[5*a[1],3*a[1]],[8*a[1],15*a[1]],[10*a[1],5*a[1],12*a[1],9*a[1],6*a[1],3*a[1]],[5*a[1],10*a[1],15*a[1],3*a[1],6*a[1],9*a[1],12*a[1]],1/(1-q)],

[I36,[6*a[1],3*a[1]],[9*a[1],18*a[1]],[12*a[1],6*a[1],15*a[1],12*a[1],9*a[1],6*a[1],3*a[1]],[6*a[1],12*a[1],18*a[1],3*a[1],6*a[1],9*a[1],12*a[1],15*a[1]],1/(1-q)],

[I44,[4*a[1],4*a[1]],[8*a[1],16*a[1]],[12*a[1],8*a[1],4*a[1],12*a[1],8*a[1],4*a[1]],
[4*a[1],8*a[1],12*a[1],16*a[1],4*a[1],8*a[1],12*a[1]],1/(1-q)],

[I45,[5*a[1],4*a[1]],[9*a[1],20*a[1]],[15*a[1],10*a[1],5*a[1],16*a[1],12*a[1],8*a[1],4*a[1]],
[5*a[1],10*a[1],15*a[1],20*a[1],4*a[1],8*a[1],12*a[1],16*a[1]],1/(1-q)],

[III22,[a[1],a[2]],[2*a[1],a[1]+a[2],2*a[2]],
[2*a[1]-a[1],2*a[1]-a[2],2*a[2]-a[1],2*a[2]-a[2]],[a[1],a[2]],1/((1-q)*(1-q^2))],

[III23,[a[1],a[2]],[2*a[1],a[1]+a[2],3*a[2]],
[2*a[1]-a[1],2*a[1]-a[2],2*a[1]-2*a[2],3*a[2]-a[1],3*a[2]-a[2],3*a[2]-2*a[2]],
[a[1],a[2],2*a[2]],1/(1-q)^2],

[III24,[a[1],a[2]],[2*a[1],a[1]+a[2],4*a[2]],
[2*a[1]-a[1],2*a[1]-a[2],2*a[1]-2*a[2],2*a[1]-3*a[2],4*a[2]-a[1],4*a[2]-a[2],4*a[2]-2*a[2],4*a[2]-3*a[2]],
[a[1],a[2],2*a[2],3*a[2]],1/(1-q)^2],

[III25,[a[1],a[2]],[2*a[1],a[1]+a[2],5*a[2]],
[2*a[1]-a[1],2*a[1]-a[2],2*a[1]-2*a[2],2*a[1]-3*a[2],2*a[1]-4*a[2],5*a[2]-a[1],5*a[2]- a[2],5*a[2]-2*a[2],5*a[2]-3*a[2],5*a[2]-4*a[2]],
[a[1],a[2],2*a[2],3*a[2],4*a[2]],1/(1-q)^2],

[III26,[a[1],a[2]],[2*a[1],a[1]+a[2],6*a[2]],
[2*a[1]-a[1],2*a[1]-a[2],2*a[1]-2*a[2],2*a[1]-3*a[2],2*a[1]-4*a[2],2*a[1]-5*a[2],6*a[2]-a[1],6*a[2]-a[2],6*a[2]-2*a[2],6*a[2]-3*a[2],6*a[2]-4*a[2],6*a[2]-5*a[2]],
[a[1],a[2],2*a[2],3*a[2],4*a[2],5*a[2]],1/(1-q)^2],

[III27,[a[1],a[2]],[2*a[1],a[1]+a[2],7*a[2]],
[2*a[1]-a[1],2*a[1]-a[2],2*a[1]-2*a[2],2*a[1]-3*a[2],2*a[1]-4*a[2],2*a[1]-5*a[2],2*a[1]-6*a[2],7*a[2]-a[1],7*a[2]-a[2],7*a[2]-2*a[2],7*a[2]-3*a[2],7*a[2]-4*a[2],7*a[2]-5*a[2],7*a[2]-6*a[2]],
[a[1],a[2],2*a[2],3*a[2],4*a[2],5*a[2],6*a[2]],1/(1-q)^2],

[III33,[a[1],a[2]],[3*a[1],a[1]+a[2],3*a[2]],
[3*a[1]-a[1],3*a[1]-2*a[1],3*a[1]-a[2],3*a[1]-2*a[2],3*a[2]-a[1],3*a[2]-2*a[1],3*a[2]-a[2],3*a[2]-2*a[2]],
[a[1],2*a[1],a[2],2*a[2]],1/((1-q)*(1-q^2))],

[III34,[a[1],a[2]],[a[1]+a[2],3*a[1],4*a[2]],
[3*a[1]-a[1],3*a[1]-2*a[1],3*a[1]-a[2],3*a[1]-2*a[2],3*a[1]-3*a[2],4*a[2]-a[1],4*a[2]-2*a[1],4*a[2]-a[2],4*a[2]-2*a[2],4*a[2]-3*a[2]],[a[1],2*a[1],a[2],2*a[2],3*a[2]],1/(1-q)^2],

[III35,[a[1],a[2]],[a[1]+a[2],3*a[1],5*a[2]],
[3*a[1]-a[1],3*a[1]-2*a[1],3*a[1]-a[2],3*a[1]-2*a[2],3*a[1]-3*a[2],3*a[1]-4*a[2],5*a[2]-a[1],5*a[2]-2*a[1],5*a[2]-a[2],5*a[2]-2*a[2],5*a[2]-3*a[2],5*a[2]-4*a[2]],[a[1],2*a[1],a[2],2*a[2],3*a[2],4*a[2]],1/(1-q)^2],

[III36,[a[1],a[2]],[a[1]+a[2],3*a[1],5*a[2]],
[3*a[1]-a[1],3*a[1]-2*a[1],3*a[1]-a[2],3*a[1]-2*a[2],3*a[1]-3*a[2],3*a[1]-4*a[2],3*a[1]-5*a[2],6*a[2]-a[1],6*a[2]-2*a[1],6*a[2]-a[2],6*a[2]-2*a[2],6*a[2]-3*a[2],6*a[2]-4*a[2],6*a[2]-5*a[2]],[a[1],2*a[1],a[2],2*a[2],3*a[2],4*a[2],5*a[2]],1/(1-q)^2],

[III44,[a[1],a[2]],[a[1]+a[2],4*a[1],4*a[2]],
[4*a[1]-a[1],4*a[1]-2*a[1],4*a[1]-3*a[1],4*a[1]-a[2],4*a[1]-2*a[2],4*a[1]-3*a[2],4*a[2]-a[1],4*a[2]-2*a[1],4*a[2]-3*a[1],4*a[2]-a[2],4*a[2]-2*a[2],4*a[2]-3*a[2]],[a[1],2*a[1],3*a[1],a[2],2*a[2],3*a[2]],1/((1-q)*(1-q^2))],

[III45,[a[1],a[2]],[a[1]+a[2],4*a[1],5*a[2]],
[4*a[1]-a[1],4*a[1]-2*a[1],4*a[1]-3*a[1],4*a[1]-a[2],4*a[1]-2*a[2],4*a[1]-3*a[2],4*a[1]-4*a[2],5*a[2]-a[1],5*a[2]-2*a[1],5*a[2]-3*a[1],5*a[2]-a[2],5*a[2]-2*a[2],5*a[2]-3*a[2],5*a[2]-4*a[2]],[a[1],2*a[1],3*a[1],a[2],2*a[2],3*a[2],4*a[2]],1/(1-q)^2],

[C3,[a[1],a[2],a[3]],[2*a[1],2*a[2],2*a[3],a[1]+a[2],a[1]+a[3],a[2]+a[3]],
[2*a[1]-a[2],2*a[1]-a[3],2*a[2]-a[1],2*a[2]-a[2],2*a[2]-a[3],2*a[3]-a[1],2*a[3]-a[2],2*a[3]-a[3],a[1]+a[2]-a[2],
a[1]+a[2]-a[3],a[1]+a[3]-a[2],a[1]+a[3]-a[3],a[2]+a[3]-a[1],a[2]+a[3]-a[2],a[2]+a[3]-a[3]],[a[1],a[2],a[3]],1/((1-q)*(1-q^2)*(1-q^3))],

[B4,[a[1],a[2]],[2*a[1],a[1]+2*a[2],3*a[2]],
[2*a[1]-a[1],2*a[1]-a[2],2*a[1]-2*a[2],a[1]+2*a[2]-a[1],a[1]+2*a[2]-a[2], a[1]+2*a[2]-a[1]-a[2],3*a[2]-a[1],3*a[2]-a[2],3*a[2]-a[1]-a[2]],[a[1],a[2],a[1]+a[2],2*a[2]],1/(1-q)^2],

[C41,[a[1],a[1],a[1]],[2*a[1],2*a[1],2*a[1],2*a[1],2*a[1]],
[a[1],a[1],a[1],a[1],a[1],a[1],a[1],a[1],a[1],a[1],a[1],a[1]],[a[1],a[1],a[1],2*a[1]],
1/((1-q)*(1-q^2))], # but WHY ??? shouldn’t be # O(3,C)=O(3,R) Z[p_1] ? or 1/((1-q)*(1-q^2))

[C42,[a[1],a[2],a[3]],[2*a[1],2*a[2],2*a[3],a[1]+a[3],a[2]+a[3]],[2*a[1]-a[2],2*a[1]-a[3],2*a[2]-a[1],2*a[2]-a[3],2*a[3]-a[1],2*a[3]-a[2],2*a[3]-a[3],
2*a[3]-a[1]-a[2],a[1]+a[3]-a[2],a[1]+a[3]-a[3],a[2]+a[3]-a[1],a[3],a[2]],[a[1],a[1]+a[2],a[2],a[3]],1/((1-q)^2*(1-q^2))],

[C43,[a[1],a[2],a[3]],[2*a[1],2*a[2],3*a[3],a[1]+a[2],a[1]+a[3],a[2]+a[3]],[2*a[1]-a[2],2*a[1]-a[3],2*a[1]-2*a[3],2*a[2]-a[1],
2*a[2]-a[2],2*a[2]-a[3],2*a[2]-2*a[3],3*a[3]-a[1],3*a[3]-a[2],3*a[3]-a[3],a[1]+a[2]-a[2],a[1]+a[2]-a[3],a[1]+a[2]-2*a[3],a[1]+a[3]-a[1],
a[1]+a[3]-a[2],a[1]+a[3]-a[3],a[2]+a[3]-a[1],a[2]+a[3]-a[2],a[2]+a[3]-a[3]],[a[1],a[2],a[3],2*a[3]],1/((1-q)^2*(1-q^2))],

[D4,[0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[seq(0,i=1..36)],[0,0,0,0],1/((1-q)*(1-q^2)*(1-q^3)*(1-q^4))], # to be typed in one nice day

[B51,[a[1],a[2]],[2*a[1],3*a[2]],[2*a[1]-a[2],2*a[1]-2*a[2],3*a[2]-a[1],3*a[2]-a[2],3*a[2]-a[1]-a[2]],
[a[1],a[2],a[1]+a[2],2*a[2],a[1]+2*a[2]],1/(1-q)^2],

[B52,[3*a[1],2*a[1]],[6*a[1],7*a[1],8*a[1]],[a[1],2*a[1],2*a[1],3*a[1],3*a[1],4*a[1],4*a[1],4*a[1],5*a[1],5*a[1],6*a[1]],[2*a[1],3*a[1],4*a[1],5*a[1],6*a[1]],1/(1-q)],

[B53,[a[1],a[2]],[2*a[1],a[1]+2*a[2],4*a[2]],
[2*a[1]-a[1],2*a[1]-a[2],2*a[1]-2*a[2],2*a[1]-a[1]-a[2],2*a[1]-3*a[2],a[1]+2*a[2]-a[1],a[1]+2*a[2]-a[2], a[1]+2*a[2]-a[1]-a[2],4*a[2]-a[1],4*a[2]-a[2],
4*a[2]-a[1]-a[2],4*a[2]-2*a[2]],[a[1],a[2],a[1]+a[2],2*a[2],3*a[2]],1/(1-q)^2],

[B54,[a[1],a[2]],[3*a[1],2*a[1]+a[2],a[1]+2*a[2],3*a[2]],[3*a[1]-a[1],3*a[1]-a[1]-a[2],3*a[1]-a[2],3*a[1]-2*a[2],2*a[1]+a[2]-a[1],2*a[1]+a[2]-a[1]-a[2],2*a[1]+a[2]-a[2],2*a[1]+a[2]-2*a[2],a[1]+2*a[2]-a[1],a[1]+2*a[2]-2*a[1],a[1]+2*a[2]-a[1]-a[2],a[1]+2*a[2]-a[2],a[1]+2*a[2]-2*a[2],3*a[2]-a[1],3*a[2]-2*a[1],3*a[2]-a[1]-a[2],3*a[2]-a[2],3*a[2]-2*a[2]],[a[1],a[2],2*a[1],a[1]+a[2],2*a[2]],1/((1-q)*(1-q^2))],

[C51,[a[1],a[1],a[1]],[2*a[1],2*a[1],2*a[1],2*a[1]],[a[1],a[1],a[1],a[1],a[1],a[1],a[1],a[1],a[1]],[a[1],a[1],a[1],2*a[1],2*a[1]],1/(1-q)],

[C52,[a[1],a[2],a[2]],[2*a[1],2*a[2],2*a[2],a[1]+a[2]],[2*a[1]-a[1],2*a[1]-a[2],2*a[1]-a[2],2*a[1]-2*a[2],2*a[2]-a[1],2*a[2]-a[2],2*a[2]-a[2],2*a[2]-a[1],2*a[2]-a[2],a[1]],[a[1],a[2],a[2],a[1]+a[2],2*a[2]],1/(1-q)^2],

[C53,[3*a[1],3*a[2],a[1]+a[2]],[6*a[1],3*a[1]+3*a[2],6*a[2],4*a[1]+a[2],a[1]+4*a[2]],[6*a[1]-3*a[2],6*a[1]-a[1]-a[2],6*a[1]-2*a[1]-2*a[2],3*a[1]+3*a[2]-3*a[2],3*a[1]+3*a[2]-a[1]-a[2],6*a[2]-3*a[1],6*a[2]-3*a[2],6*a[2]-a[1]-a[2],6*a[2]-2*a[1]-2*a[2],4*a[1]+a[2]-3*a[1],4*a[1]+a[2]-3*a[2],4*a[1]+a[2]-a[1]-a[2],a[1]+4*a[2]-3*a[1],a[1]+4*a[2]-3*a[2],a[1]+4*a[2]-a[1]-a[2]],[3*a[1],3*a[1]+3*a[2],3*a[2],a[1]+a[2],2*a[1]+2*a[2]],1/((1-q)*(1-q^2))],

[C54,[a[1],a[2],2*a[1]-a[2]],[2*a[1],3*a[1]-a[2],2*a[2],4*a[1]-2*a[2]],[a[1],2*a[1]-a[2],a[2],2*a[1]-a[2],3*a[1]-2*a[2],2*a[2]-a[1],3*a[2]-2*a[1],3*a[1]-2*a[2],4*a[1]-3*a[2],3*a[1]-3*a[2],2*a[1]-2*a[2]],[a[1],a[2],2*a[1]-a[2],2*a[1],a[1]+a[2]],1/(1-q)^2],

[C55,[a[1],a[2],a[3]],[a[1]+a[2],a[1]+a[3],2*a[2],2*a[3],3*a[1]],
[a[1]+a[2]-a[2],a[1]+a[2]-a[3],a[1]+a[3]-a[2],a[1]+a[3]-a[3],2*a[2]-a[1],2*a[2]-2*a[1],2*a[2]-a[2],
2*a[2]-a[3],2*a[3]-a[1],2*a[3]-2*a[1],2*a[3]-a[2],2*a[3]-a[3],3*a[1]-a[1],3*a[1]-a[2],3*a[1]-a[2]-a[3],3*a[1]-a[3]],[a[1],2*a[1],a[2],a[2]+a[3],a[3]],
1/((1-q)^2*(1-q^2))],

[C56,[2*a[1],3*a[1],a[2]],[6*a[1],2*a[2],5*a[1],2*a[1]+a[2],3*a[1]+a[2]],
[6*a[1]-2*a[1],6*a[1]-3*a[1],6*a[1]-a[2],2*a[2]-2*a[1],2*a[2]-4*a[1],2*a[2]-3*a[1],2*a[2]-6*a[1],2*a[2]-a[2],5*a[1]-3*a[1],5*a[1]-a[2],
2*a[1]+a[2]-3*a[1],2*a[1]+a[2]-a[2],3*a[1]+a[2]-2*a[1],3*a[1]+a[2]-4*a[1],3*a[1]+a[2]-3*a[1],3*a[1]+a[2]-a[2]],
[2*a[1],4*a[1],3*a[1],6*a[1],a[2]],1/(1-q)^2],

[C57,[2*a[1],a[1]+a[2],2*a[2]],[3*a[1]+a[2],a[1]+3*a[2],4*a[2],2*a[1]+2*a[2],6*a[1]],[3*a[1]+a[2]-a[1]-a[2],3*a[1]+a[2]-2*a[2],a[1]+3*a[2]-2*a[1],a[1]+3*a[2]-4*a[1],a[1]+3*a[2]-a[1]-a[2],a[1]+3*a[2]-2*a[2],4*a[2]-2*a[1],4*a[2]-4*a[1],4*a[2]-2*a[1]-2*a[2],4*a[2]-a[1]-a[2],4*a[2]-2*a[2],2*a[1]+2*a[2]-a[1]-a[2],2*a[1]+2*a[2]-2*a[2],6*a[1]-2*a[1],6*a[1]-2*a[1]-2*a[2],6*a[1]-a[1]-a[2],6*a[1]-2*a[2]],[2*a[1],4*a[1],2*a[1]+2*a[2],a[1]+a[2],2*a[2]],1/(1-q)^2],

[C58,[a[1],a[2],a[3]],[2*a[1],2*a[2],2*a[3],a[1]+a[2]],[2*a[1]-a[2],2*a[1]-a[2]-a[3],2*a[1]-a[3],2*a[2]-a[1],2*a[2]-a[1]-a[3],2*a[2]-a[2],2*a[2]-a[2]-a[3],2*a[2]-a[3],2*a[3]-a[1],2*a[3]-a[2],a[1]+a[2]-a[2],a[1]+a[2]-a[2]-a[3],a[1]+a[2]-a[3]],[a[1],a[1]+a[3],a[2],a[2]+a[3],a[3]],1/((1-q)*(1-q)*(1-q^2))],

[C59,[a[1],a[2],a[3]],[2*a[1],a[1]+a[2],2*a[2],a[1]+a[3],a[2]+a[3],4*a[3]],[2*a[1]-a[2],2*a[1]-a[3],2*a[1]-2*a[3],2*a[1]-3*a[3],
a[1]+a[2]-a[2],a[1]+a[2]-a[3],a[1]+a[2]-2*a[3],a[1]+a[2]-3*a[3],2*a[2]-a[1],2*a[2]-a[2],2*a[2]-a[3],2*a[2]-2*a[3],2*a[2]-3*a[3],
a[1]+a[3]-a[1],a[1]+a[3]-a[2],a[1]+a[3]-a[3],a[2]+a[3]-a[1],a[2]+a[3]-a[2],a[2]+a[3]-a[3],4*a[3]-a[1],4*a[3]-a[2],4*a[3]-a[3],
4*a[3]-2*a[3]],[a[1],a[2],a[3],2*a[3],3*a[3]],1/((1-q)*(1-q)*(1-q^2))],

[C510, [a[1],a[2],a[3]],[2*a[1],a[1]+a[2],a[1]+a[3],a[2]+a[3],3*a[2],3*a[3]],[2*a[1]-a[2],2*a[1]-2*a[2],2*a[1]-a[3],2*a[1]-2*a[3],a[1]+a[2]-a[1],a[1]+a[2]-a[2],a[1]+a[2]-a[3],a[1]+a[2]-2*a[3],a[1]+a[3]-a[1],a[1]+a[3]-a[2],a[1]+a[3]-2*a[2],a[1]+a[3]-a[3],a[2]+a[3]-a[1],a[2]+a[3]-a[2],a[2]+a[3]-a[3],3*a[2]-a[1],3*a[2]-a[2],3*a[2]-a[3],3*a[2]-2*a[3],3*a[3]-a[1],3*a[3]-a[2],3*a[3]-2*a[2],3*a[3]-a[3]],[a[1],a[2],a[3],2*a[2],2*a[3]],1/((1-q)*(1-q)*(1-q^2))],

[C511,[a[1],a[2],a[3]],[2*a[1],a[1]+a[2],a[1]+a[3],2*a[2],a[2]+2*a[3],3*a[3]],
[2*a[1]-a[2],2*a[1]-a[2]-a[3],2*a[1]-a[3],2*a[1]-2*a[3], a[1]+a[2]-a[1],a[1]+a[2]-a[2],a[1]+a[2]-a[3],a[1]+a[2]-2*a[3],
a[1]+a[3]-a[1],a[1]+a[3]-a[2],a[1]+a[3]-a[3],a[1]+a[3]-2*a[3],
2*a[2]-a[1],2*a[2]-a[2],2*a[2]-a[3],2*a[2]-2*a[3],
a[2]+2*a[3]-a[1],a[2]+2*a[3]-a[2],a[2]+2*a[3]-a[3],
3*a[3]-a[1],3*a[3]-a[2],3*a[3]-a[2]-a[3],3*a[3]-a[3],3*a[3]-2*a[3]],
[a[1],a[2],a[3],a[2]+a[3],2*a[3]],
1/(1-q)^3],

[D51,[a[1],a[3]-a[1],a[2],a[3]-a[2]],[2*a[1],2*a[3]-2*a[1],2*a[2],2*a[3]-2*a[2],a[3],a[1]+a[2],a[1]-a[2]+a[3],-a[1]+a[2]+a[3],-a[1]-a[2]+2*a[3]],
[2*a[1]-a[3]+a[1],2*a[1]-a[2],2*a[1]-a[3]+a[2],
2*a[3]-2*a[1]-a[1],2*a[3]-2*a[1]-a[3]+a[1],2*a[3]-2*a[1]-a[2],2*a[3]-2*a[1]-a[3]+a[2],
2*a[2]-a[1],2*a[2]-a[3]+a[1],2*a[2]-a[2],2*a[2]-a[3]+a[2],2*a[3]-2*a[2]-a[1],2*a[3]-2*a[2]-a[3]+a[1],2*a[3]-2*a[2]-a[2],
2*a[3]-2*a[2]-a[3]+a[2],a[3]-a[3]+a[1],a[3]-a[2],a[3]-a[3]+a[2],a[1]+a[2]-a[3]+a[1],a[1]+a[2]-a[2],a[1]+a[2]-a[3]+a[2],
a[1]-a[2]+a[3]-a[3]+a[1],a[1]-a[2]+a[3]-a[2],a[1]-a[2]+a[3]-a[3]+a[2],-a[1]+a[2]+a[3]-a[1],-a[1]+a[2]+a[3]-a[3]+a[1],-a[1]+a[2]+a[3]-a[2],-a[1]+a[2]+a[3]-a[3]+a[2],
-a[1]-a[2]+2*a[3]-a[1],-a[1]-a[2]+2*a[3]-a[3]+a[1],-a[1]-a[2]+2*a[3]-a[2],-a[1]-a[2]+2*a[3]-a[3]+a[1]],
[a[1],a[3]-a[1],a[2],a[3]-a[2],a[3]],1/((1-q)*(1-q^2)*(1-q^4))], #(1-q+q^2)/( (1-q)^2*(1-q^2)*(1-q^4) )

[D52,[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],1/((1-q)^2*(1-q^2))], # to be typed in one nice day; 1/((1-q)*(1-q)*(1-q^2)*(1-q^3))

[D53,[0,0,0,0],[0,0,0,0,0,0,0,0,0],[seq(0,i=1..35)],[0,0,0,0,0],1/((1-q)^2*(1-q^2)^2)], # to be typed in one nice day

[D54,[0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[seq(0,i=1..43)],[0,0,0,0,0],1/((1-q)^2*(1-q^2)*(1-q^3))], # to be typed in one nice day

[E5,[0,0,0,0,0],[seq(0,i=1..15)],[seq(0,i=1..70)],[0,0,0,0,0],1/((1-q)*(1-q^2)*(1-q^3)*(1-q^4)*(1-q^5))],# to be typed in one nice day

[B6,[3*a[1],2*a[1]],[6*a[1],7*a[1]],[3*a[1],4*a[1],a[1],2*a[1],4*a[1],5*a[1]],
[3*a[1],2*a[1],6*a[1],5*a[1],4*a[1],8*a[1]] ,1/(1-q)],

[C6,[3*a[1],3*a[1],2*a[1]],[6*a[1],6*a[1],5*a[1],5*a[1]],[3*a[1],3*a[1],4*a[1],3*a[1],3*a[1],4*a[1],2*a[1],2*a[1],2*a[1],2*a[1],2*a[1]],
[3*a[1],3*a[1],2*a[1],6*a[1],6*a[1],4*a[1]],1/(1-q)]