Full paper in PDF format:
$%M. Loaiza and H. Upmeier, Toeplitz C*-algebras on super-Cartan domains, Rev. Mat. Complut. 21 (2008), no. 2, 489–518.%$

Toeplitz C*-Algebras on Super-Cartan Domains
Maribel LOAIZA and Harald UPMEIER
Departamento de Matemáticas
CINVESTAV
Apartado Postal 14-740 07000
México D.F. — Mexico
mloaiza@math.cinvestav.mx
Fachbereich Mathematik und Informatik
Universität Marburg
35032 Marburg — Germany
upmeier@mathematik.uni-marburg.de
Received: August 1, 2007
Accepted: December 21, 2007

ABSTRACT

We study Hilbert spaces of super-holomorphic functions (including anti-commuting Grassmann variables) in the setting of bounded symmetric domains, more precisely for the matrix ball of arbitrary size. Our main results concern the classification of irreducible representations of the associated Toeplitz C* -algebra and an explicit decomposition of the super-Bergman space as a direct sum of vector-valued (ordinary) Bergman spaces.

Key words: Toeplitz operator algebras, Grassmann variables, supersymmetry, Berezin quantization, Cartan domains, vector-valued Bergman spaces.
2000 Mathematics Subject Classification: 47L80, 32M15.