One-character extension characters of tensor products of small CFTs organize into compact S-invariant polynomial bases, yielding closed forms up to central charge 128 and conjectured new one-character CFTs.
A mass formula for unimodular lattices with no roots
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abstract
We derive a mass formula for n-dimensional unimodular lattices having any prescribed root system. We use Katsurada's formula for the Fourier coefficients of Siegel Eisenstein series to compute these masses for all root systems of even unimodular 32-dimensional lattices and odd unimodular lattices of dimension n < 31. In particular, we find the mass of even unimodular 32-dimensional lattices with no roots, and the mass of odd unimodular lattices with no roots in dimension n < 31, verifying Bacher and Venkov's enumerations in dimensions 27 and 28. We also compute better lower bounds on the number of inequivalent unimodular lattices in dimensions 26 to 30 than those afforded by the Minkowski-Siegel mass constants. The ASCII text file table.txt (1.3 MB) at arXiv:math.NT/0012231 includes the complete table of masses of 32-dimensional even unimodular lattices with any given root system, and may be dowloaded using the source link.
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Tensor Product CFTs and One-Character Extensions
One-character extension characters of tensor products of small CFTs organize into compact S-invariant polynomial bases, yielding closed forms up to central charge 128 and conjectured new one-character CFTs.