Minimal representations of conformal groups and generalized Laguerre functions / Jan Möllers. 2010
Content
- Introduction
- Jordan theory
- Jordan algebras
- Peirce decomposition
- The constants and
- The structure group and its Lie algebra
- Orbits of the structure group and equivariant measures
- The conformal group
- The Kantor–Koecher–Tits construction
- The universal covering
- Root space decomposition
- k-representations with a kl-spherical vector
- The Bessel operators
- Minimal representations of conformal groups
- Construction of the minimal representation
- Infinitesimal representations on C(O)
- Construction of the (g,k)-module
- Integration of the (g,k)-module
- Two prominent examples
- Generalized principal series representations
- The k-Casimir
- The unitary inversion operator FO
- Generalized Laguerre functions
- The fourth order differential operator D,
- The generating functions Gi,(t,x)
- The eigenfunctions i,j,(x)
- Integral representations
- Orthogonal polynomials
- Recurrence relations
- Meijer's G-transform
- Applications to minimal representations
- Tables of simple real Jordan algebras
- Structure constants of V
- Structure constants of V+
- The constants and
- Conformal algebra and structure algebra
- Calculations in rank 2
- Parabolic subgroups
- Special Functions
- Bibliography
- Notation Index
- Subject Index