The term "Hecke algebra" can refer to several related but distinct concepts in mathematics, particularly in the fields of number theory, representation theory, and algebra. Here are a few notable interpretations: 1. **Hecke Algebras in Representation Theory**: In this context, Hecke algebras arise in the study of algebraic groups and their representations. They are associated with Coxeter groups and provide a way to study representations of symmetric groups and general linear groups.
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