
Chapter 9
The q-Deformed Generalized Weyl Algebra
In this chapter a q-deformation of the generalized Weyl algebra A
s;h
defined in Chapter 8
is introduced. Its generators U and V satisfy UV − qV U = hV
s
, and it will be denoted
by A
s;h|q
. As in the preceding chapters, we will be interested in ordering results for words
in the generators U and V . In particular, we introduce associated q-deformed generalized
Stirling and Bell numbers and derive some of their properties. As it will turn out, the study
of A
s;h|q
is significantly more difficult than the undeformed case, and explicit expressions
will be given only for special cases. As in the undeformed case we ...