On Lie algebraic properties of the step operators acting on P or confluent P functions

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Abstract
P functions and confluent P (CP) functions are classified into two and five groups respectively according to the types of the step operators (SO’s) intrinsic to the respective classes of functions. The correspondence between the types of the SO’s and the realizations of the Lie algebras G (a,b) and T6 is established as follows. The modified SO’s acting on P functions (SOP’s) belong to either of the type A and E realizations of G (1,0) and T6 respectively. The modified SOC’s, namely the SO’s acting on CP functions, belong to one of the type B, C′, C″, F, D′ realizations of G (1,0), G (0,1), G (0,0), or T6.

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