John Ryan
Department of Mathematics, University of Arkansas, Fayetteville, AR 72701
Ahlfors matrices, fundamental domains in n
real variables and hyperbolic Dirac operators
In this talk we will use a construction of Ahlfors using Clifford algebras
to construct Möbius transformations in n real
variables. These in turn will be used to introduce analogues of fundamental
domains for analogues of subgroups of the modular group, SL(2,Z).
These are examples of conformally flat manifolds. A Dirac operator with
respect to the hyperbolic metric on these spaces will be set up and the
function theory, including Hardy spaces, for these operators will be examined.