In mathematics, the Hecke algebra of a pair (G, K) of locally compact or reductive Lie groups is an algebra of measures under convolution. It can also be defined for a pair (g, K) of a maximal compact subgroup K of a Lie group with Lie algebra g, in which case the Hecke algebra is an algebra with an approximate identity, whose approximately unital modules are the same as K-finite representations of the pairs (g, K).
In mathematics, the Hecke algebra of a pair (G, K) of locally compact or reductive Lie groups is an algebra of measures under convolution. It can also be defined for a pair (g, K) of a maximal compact subgroup K of a Lie group with Lie algebra g, in which case the Hecke algebra is an algebra with an approximate identity, whose approximately unital modules are the same as K-finite representations of the pairs (g, K).
Source: Wikipedia "Hecke algebra of a pair" · CC BY-SA 4.0
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