Cuspidal irreducible complex or l-modular representations of quaternionic forms of p-adic classical groups for odd p

Skodlerack Daniel

摘要

Abstract Given a quaternionic form Gdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{G}$$end{document} of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of Gdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{G}$$end{document} with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At first: Every irreducible cuspidal representation of Gdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{G}$$end{document} is induced from a cuspidal type, i.e. from a certain irreducible representation of a compact open subgroup of Gdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{G}$$end{document}, constructed from a βdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$beta $$end{document}-extension and a cuspidal representation of a finite group. Secondly we show that two intertwining cuspidal types of Gdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{G}$$end{document} are up to equivalence conjugate under some element of Gdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{G}$$end{document}.

Cuspidal irreducible complex or l-modular representations of quaternionic forms of p-adic classical groups for odd p

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