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Lie Group Quantum Mathematics Seminar

 Imaginary reflections and automorphisms of the monster Lie algebra

 Lisa Carbone, Rutgers University

Location:  Hill 705
Date & time: Friday, 19 April 2019 at 12:00PM - 1:00PM

  • Abstract:  We describe a `hidden symmetry' of the root lattice of the monster Lie algebra m, namely a reflection with respect to an imaginary simple root, that preserves the bilinear form and root multiplicities. This symmetry appears only after the infinite root lattice is specialized to the unique even 2-dimensional unimodular Lorentzian lattice II_{1,1}. When composed with reflection in the unique real simple root, this symmetry extends to the Cartan involution on m. We describe an uncountable family of Cartan involutions and their associated eigenspaces, known as Cartan pairs, and examine these involutions as elements of Aut(m).

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