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2 results

  • BGG reciprocity for current algebras

  • Part of
  • Vyjayanthi Chari, Bogdan Ion
  • Journal:
    Compositio Mathematica / Volume 151 / Issue 7 / July 2015
    Published online by Cambridge University Press:
    09 February 2015, pp. 1265-1287
    Print publication:
    July 2015
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  • In Bennett et al. [BGG reciprocity for current algebras, Adv. Math. 231 (2012), 276–305] it was conjectured that a BGG-type reciprocity holds for the category of graded representations with finite-dimensional graded components for the current algebra associated to a simple Lie algebra. We associate a current algebra to any indecomposable affine Lie algebra and show that, in this generality, the BGG reciprocity is true for the corresponding category of representations.

  • A Plancherel formula for Sp2n/Spn×Spn and its application

  • Part of
  • Zhengyu Mao, Stephen Rallis
  • Journal:
    Compositio Mathematica / Volume 145 / Issue 2 / March 2009
    Published online by Cambridge University Press:
    01 March 2009, pp. 501-527
    Print publication:
    March 2009
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  • We compute the spherical functions on the symmetric space Sp2n/Spn×Spn and derive a Plancherel formula for functions on the symmetric space. As an application of the Plancherel formula, we prove an identity which amounts to the fundamental lemma of a relative trace identity between Sp2n and .