Vk. Dobrev et al., A Q-SCHRODINGER ALGEBRA, ITS LOWEST-WEIGHT REPRESENTATIONS AND GENERALIZED Q-DEFORMED HEAT SCHRODINGER EQUATIONS/, Journal of physics. A, mathematical and general, 29(18), 1996, pp. 5909-5918
We construct a q-deformation (S) over cap(q) of the centrally-extended
Schrodinger algebra (S) over cap and an algebraic representation theo
ry through lowest-weight representations. We use Verma modules over (S
) over cap(q), calculate their singular vectors and factorize the Verm
a modules by submodules built on the singular vectors. We also give a
realization of (S) over cap(q) with q-difference operators and obtain
a polynomial realization of the lowest-weight representations and an i
nfinite family of q-difference equations which may be called generaliz
ed q-deformed heat/Schrodinger equations. We also apply our methods to
the on-shell q-Schrodinger algebra proposed by Floreanini and Vinet.