Q-Schroedinger algebra, its lowest weight representations and generalized q-deformed heat equations

摘要

We give a q-deformation S-perpendicular(sub q) of the centrally extended Schroedinger algebra. We construct the lowest weight representations of S-perpendicular(sub q), starting from the Verma modules over S-perpendicular(sub q), finding their singular vectors and factoring the Verma submodules built on the singular vectors. We also give a vector-field realization of S-perpendicular(sub q) which provides polynomial realization of the lowest weight representations and an infinite hierarchy of q-difference equations which may be called generalized q-deformed heat equations. We also apply our methods to the on-shell q-Schroedinger algebra proposed by Floreanini and Vinet. (author). 12 refs. (Atomindex citation 27:046058)