Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-07-11
Physics
High Energy Physics
High Energy Physics - Theory
83 pages; v4: Directors' cut edition: misprints corrected, improved figures, improved notations for quaternionic vielbein
Scientific paper
10.1007/s00220-008-0563-9
Quasi-conformal actions were introduced in the physics literature as a generalization of the familiar fractional linear action on the upper half plane, to Hermitian symmetric tube domains based on arbitrary Jordan algebras, and further to arbitrary Freudenthal triple systems. In the mathematics literature, quaternionic discrete series unitary representations of real reductive groups in their quaternionic real form were constructed as degree 1 cohomology on the twistor spaces of symmetric quaternionic-Kahler spaces. These two constructions are essentially identical, as we show explicitly for the two rank 2 cases SU(2,1) and G_{2(2)}. We obtain explicit results for certain principal series, quaternionic discrete series and minimal representations of these groups, including formulas for the lowest K-types in various polarizations. We expect our results to have applications to topological strings, black hole micro-state counting and to the theory of automorphic forms.
Gunaydin Murat
Neitzke Andrew
Pavlyk Oleksandr
Pioline Boris
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