We study the local Hecke algebra H-G(K) for G = GL(n) and K a non-archimedean local field of characteristic zero. We show that for G = GL(2) and any two such fields K and L, there is a Morita equivalence H-G(K) similar to(M) H-G(L), by using the Bernstein decomposition of the Hecke algebra and determining the intertwining algebras that yield the Bernstein blocks up to Morita equivalence. By contrast, we prove that for G = GL(n), there is an algebra isomorphism H-G(K) congruent to H-G(L) which is an isometry for the induced L-1-norm if and only if there is a field isomorphism K congruent to L.
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