The OEIS is supported by the many generous donors to the OEIS Foundation.


(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A287944 Theta series of the 42-dimensional lattice of hyper-roots A_5(SU(3)). 9
1, 0, 0, 896, 11856, 154368, 2331648, 27065088, 281311128 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..8.

R. 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.


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

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


Cf. A008434. {D_6}^{+} lattice is rescaled A_1(SU(3)).

Cf. A290654 is A_2(SU(3)). Cf. A290655 is A_3(SU(3)). Cf. A287329 is A_4(SU(3). Cf. A288488, A288489, A288776, A288779, A288909.

Sequence in context: A251315 A218814 A264329 * A323964 A145498 A252378

Adjacent sequences:  A287941 A287942 A287943 * A287945 A287946 A287947




Robert Coquereaux, Sep 01 2017



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 26 03:23 EST 2022. Contains 350572 sequences. (Running on oeis4.)