Conditionally invariant (q-deformed) equations from Verma modules subsingular vectors

摘要

We give a systematic discussion of the relation between subsingular vectors of Verma modules over semisimple Lie algebras G and differential equations which are conditionally G-invariant. This is extended to the Drinfled-Jimbo q-deformation U(sub q)(G) of G. We treat the example of the conformal algebra su(2,2), its complexification sl(4) and their q-deformations. The conditionally invariant equations are the d'Alembert equation and a new equation arising from a subsingular vector proposed by Bernstein-Gel'fand-Gel'fand. We give also the q-difference analogues of these equations. (author). 15 refs. (Atomindex citation 27:023395)