Types in reductive -adic groups: The Hecke algebra of a cover |
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Authors: | Colin J. Bushnell Philip C. Kutzko |
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Affiliation: | Department of Mathematics, King's College, Strand, London WC2R 2LS, United Kingdom ; Department of Mathematics, University of Iowa, Iowa City, Iowa 52242 |
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Abstract: | In this paper, is a non-Archimedean local field and is the group of -points of a connected reductive algebraic group defined over . Also, is an irreducible representation of a compact open subgroup of , the pair being a type in . The pair is assumed to be a cover of a type in a Levi subgroup of . We give conditions, generalizing those of earlier work, under which the Hecke algebra is the tensor product of a canonical image of and a sub-algebra , for a compact open subgroup of containing . |
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Keywords: | $p$-adic reductive group type cover Hecke algebra |
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