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This paper focuses on the theory of the Hecke rings associated with thegeneral linear groups originally studied by Hecke and Shimura et al., andmoreover generalizes its notions to Hecke rings associated with theautomorphism groups of certain algebras. Then, in the case of the HeisenbergLie algebra, we show an analog of the classical theory.

A note on a Hecke ring associated with the Heisenberg Lie algebra