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- W4302184468 abstract "Let $F$ be any non archimedean locally compact field of residual characteristic $p$, let $G$ be any reductive connected $F$-group and let $K$ be any special parahoric subgroup of $G(F)$. We choose a parabolic $F$-subgroup $P$ of $G$ with Levi decomposition $P=MN$ in good position with respect to $K$. Let $C$ be an algebraically closed field of characteristic $p$. We choose an irreducible smooth $C$-representation $V$ of $K$. We investigate the natural intertwiner from the compact induced representation $ind_{K}^{G(F)}V$ to the parabolically induced representation $Ind_{P(F)}^{G(F)}(ind_{M(F) cap K}^{M(F)}V_{N(F)cap K})$. Under a regularity condition on $V$, we show that the intertwiner becomes an isomorphism after a localisation at a specific Hecke operator. When $F$ has characteristic 0, $G$ is $F$-split and $K$ is hyperspecial, the result was essentially proved by Herzig. We define the notion of $K$-supersingular irreducible smooth $C$-representation of $G(F)$ which extends Herzig's definition for admissible irreducible representations and we give a list of $K$-supersingular irreducible representations which are supercuspidal and conversely a list of supercuspidal representations which are $K$-supersingular." @default.
- W4302184468 created "2022-10-06" @default.
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- W4302184468 date "2011-11-30" @default.
- W4302184468 modified "2023-09-30" @default.
- W4302184468 title "Comparison of compact induction with parabolic induction" @default.
- W4302184468 doi "https://doi.org/10.48550/arxiv.1111.7276" @default.
- W4302184468 hasPublicationYear "2011" @default.
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