research in special function with Lie algebra

Question

First of all, I don't know if this is the right place to ask about this. If not, please direct me somewhere I can get more help.

I have to research in the field of special functions with a lie algebra There are some previous titles in this area to clarify what I mean

1) The Lie algebra of certain generating functions involving the modified hypergeometric polynomial

2) Lie- Theoretic of Some Generating Functions of Two Variable Laguerre Polynomials

3) Some Generating Functions of Jacobi Polynomials with New Parameter Lie-Group

what are the areas of this branch of mathematics and what are its uses in our lives

For the people of Experience Is this area a fertile field in which to search

With thanks for all the help

Answer 1

Try looking at Vilenkin's introductory 1968 book on Representation Theory and Special Functions. Then look at his 3 volumes on the same subject with a more detailed treatment.