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3 results

  • On some generic very cuspidal representations

  • Part of
  • Stephen DeBacker, Mark Reeder
  • Journal:
    Compositio Mathematica / Volume 146 / Issue 4 / July 2010
    Published online by Cambridge University Press:
    18 March 2010, pp. 1029-1055
    Print publication:
    July 2010
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  • Let G be a reductive p-adic group. Given a compact-mod-center maximal torus S⊂G and sufficiently regular character χ of S, one can define, following Adler, Yu and others, a supercuspidal representation π(S,χ) of G. For S unramified, we determine when π(S,χ) is generic, and which generic characters it contains.

  • Genericity of supercuspidal representations of p-adic Sp4

  • Part of
  • Corinne Blondel, Shaun Stevens
  • Journal:
    Compositio Mathematica / Volume 145 / Issue 1 / January 2009
    Published online by Cambridge University Press:
    01 January 2009, pp. 213-246
    Print publication:
    January 2009
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  • We describe the supercuspidal representations of Sp4(F), for F a non-archimedean local field of residual characteristic different from two, and determine which are generic.

  • ON REPRESENTATIONS OF QUANTUM GROUPS Uq(fm(K,H))

  • Part of
  • XIN TANG, YUNGE XU
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 78 / Issue 2 / October 2008
    Published online by Cambridge University Press:
    01 October 2008, pp. 261-284
    Print publication:
    October 2008
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  • We construct families of irreducible representations for a class of quantum groups Uq(fm(K,H). First, we realize these quantum groups as hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for Uq(fm(K,H)). Second, we study the relationship between Uq(fm(K,H)) and Uq(fm(K)). As a result, any finite-dimensional weight representation of Uq(fm(K,H)) is proved to be completely reducible. Finally, we study the Whittaker model for the center of Uq(fm(K,H)), and a classification of all irreducible Whittaker representations of Uq(fm(K,H)) is obtained.