Distribution Algebras on a p-adic Group and Lie Algebra 

(Abstract)

An indispensable tool in the representation theory of reductive Lie groups is the universal enveloping algebra of the Lie algebra of a Lie group. For p-adic groups, the Hecke algebra is a partial analogue of the enveloping algebra.

A much better analogue is the distribution algebra of left essentially compact distributions. We explain why this is so.