Near-singularity Wheeler-DeWitt wavefunctions for 5d BKL dynamics are shown to correspond to Hecke L-functions over Gaussian or Eisenstein integers, whose Euler products define complex 'primon gas' partition functions.
Hyperbolic Weyl groups and the four normed division algebras
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abstract
We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral lattices of the division algebras and associated discrete matrix groups. Our findings can be summarized by saying that the even subgroups, W^+, of the Kac-Moody Weyl groups, W, are isomorphic to generalized modular groups over K for the simply laced algebras, and to certain finite extensions thereof for the non-simply laced algebras. This hints at an extended theory of modular forms and functions.
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Wheeler-DeWitt wavefunctions for 5d BKL dynamics, automorphic L-functions and complex primon gases
Near-singularity Wheeler-DeWitt wavefunctions for 5d BKL dynamics are shown to correspond to Hecke L-functions over Gaussian or Eisenstein integers, whose Euler products define complex 'primon gas' partition functions.