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- W2964005621 abstract "We study the local Hecke algebra ({mathcal{H}_{G}(K)}) for ({G = {rm GL}_{n}}) and K a non-archimedean local field of characteristic zero. We show that for ({G = {rm GL}_{2}}) and any two such fields K and L, there is a Morita equivalence ({mathcal{H}_{G}(K) sim_{M} mathcal{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 = {rm GL}_{n}}), there is an algebra isomorphism ({mathcal{H}_{G}(K) cong mathcal{H}_{G}(L)}) which is an isometry for the induced ({L^1})-norm if and only if there is a field isomorphism ({K cong L})." @default.
- W2964005621 created "2019-07-30" @default.
- W2964005621 creator A5059989746 @default.
- W2964005621 date "2016-09-28" @default.
- W2964005621 modified "2023-10-07" @default.
- W2964005621 title "Hecke algebras for $${{rm GL}_n}$$ GL n over local fields" @default.
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- W2964005621 doi "https://doi.org/10.1007/s00013-016-0974-3" @default.
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