• Corpus ID: 15029784

Kac-Moody Fibonacci sequences, hyperbolic golden ratios, and real quadratic fields

@inproceedings{Andersen2010KacMoodyFS,
  title={Kac-Moody Fibonacci sequences, hyperbolic golden ratios, and real quadratic fields},
  author={Kasper K. S. Andersen and Lisa Carbone and Diego Penta},
  year={2010}
}
Let A be the generalized Cartan matrix of rank 2 Kac-Moody algebra g. We write g = g(a, b) when A has non-diagonal entries −a and −b. To each such A, its Weyl group and corresponding root lattice, we associate a ‘Fibonacci type ’ integer sequence. These sequences are derived from the coordinates of the real root vectors in the root space. Each element of each sequence can be expressed as a polynomial in the non-diagonal entries of the generalized Cartan matrix, whose coefficients are shallow… 

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