The minimal unitary representation of \(E_{8(8)}\). (English) Zbl 1029.17008
Summary: We give a new construction of the minimal unitary representation of the exceptional group \(E_{8(8)}\) on a Hilbert space of complex functions in 29 variables. Due to their manifest covariance with respect to the \(E_{7(7)}\) subgroup of \(E_{8(8)}\), our formulas are simpler than previous realizations and thus well suited for applications in superstring and M theory.
MSC:
| 17B25 | Exceptional (super)algebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
