Invariant Differential Operators. Volume 3: Supersymmetry

Main subject categories: • Supersymmetry • Superalgebras • Lie algebras and Lie superalgebras • Representation theory of groups • Quantum groups • Special functions • Hypergeometric functions • Global analysis, analysis on manifolds • Quantum theory

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras

Note that this volume is only half of what was originally announced, since later it turned out that the intended material would need many more pages than customary. Thus, the material was split into Volume 3 (the present one) and Volume 4. The fourth volume will cover applications of our approach to the AdS/CFT correspondence, to infinite-dimensional (super-) algebras, including (super-) Virasoro algebras, and to (q-) Schrödinger algebras.