Conditionally Invariant Equations from Subsingular Vectors

Authors: V. K. DOBREV

Abstract: We discuss the relation between subsingular vectors of Verma modules over semisimple Lie algebras {\cal G} and differential equations which are conditionally {\cal G}-invariant. We treat the example o the conformal algebra su(2,2) and its complexification sl(4). 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.