OFFSET

0,4

COMMENTS

This lattice is the k=5 member of the family of lattices of SU(3) hyper-roots associated with the fusion category A_k(SU(3)).

Simple objects of the latter are irreducible integrable representations of the affine Lie algebra of SU(3) at level k.

With k=5 there are r=(k+1)(k+2)/2=21 simple objects. The rank of the lattice is 2r=42.

The lattice is defined by 2r(k+3)^2/3=896 hyper-roots of norm 6 which are also the vectors of shortest length. Minimal norm is 6. Det =(k+3)^(3(k+1)) = 8^18.

The lattice is rescaled (q --> q^2): its theta function starts as 1 + 896*q^6 + 11856*q^8 +... See example.

LINKS

Robert Coquereaux, Theta functions for lattices of SU(3) hyper-roots, arXiv:1708.00560 [math.QA], 2017.

A. Ocneanu, The Classification of subgroups of quantum SU(N), in "Quantum symmetries in theoretical physics and mathematics", Bariloche 2000, Eds. R. Coquereaux, A. Garcia. and R. Trinchero, AMS Contemporary Mathematics, 294, pp. 133-160, (2000). End of Sec 2.5.

EXAMPLE

G.f. = 1 + 896*x^3 + 11856*x^4 + 154368*x^5 + ...

G.f. = 1 + 896*q^6 + 11856*q^8 + 154368*q^10 + ...

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Robert Coquereaux, Sep 01 2017

STATUS

approved