Modulo <i>p</i> parabolic induction of pro-<i>p</i>-Iwahori Hecke algebra

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  • Noriyuki Abe
    Creative Research Institution (CRIS) , Hokkaido University , N21, W10, Kita-ku , Sapporo , Hokkaido 001-0021 , Japan

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<jats:title>Abstract</jats:title> <jats:p>We study the structure of parabolic inductions of a pro-<jats:italic>p</jats:italic>-Iwahori Hecke algebra. In particular, we give a classification of irreducible modulo <jats:italic>p</jats:italic> representations of pro-<jats:italic>p</jats:italic>-Iwahori Hecke algebras in terms of supersingular representations. Since supersingular representations are classified by Ollivier and Vignéras, it completes the classification of irreducible modulo <jats:italic>p</jats:italic> representations. </jats:p>

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