## Current Developments in Mathematics |

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### Contents

Automorphic forms and Lie algebras | 1 |

Harmonic analysis for affine Hecke algebras | 37 |

Stability and its uses | 61 |

Copyright | |

4 other sections not shown

### Common terms and phrases

Abelian variety algebraically closed automorphic form Banach space belongs Besov space bilinear operator closed field coefficients compute conjecture constant construction corresponding definable sets definable subset definition denominator formula denote differential equations Dynkin diagram elements embeddings equivalent estimate example exists fake monster Lie Federbush's finite Morley Fourier transform fully adapted functional Banach space geometry given Hecke algebras Hrushovski implies infinite product irreducible isomorphism Kac-Moody algebras Kato's algorithm Leech lattice lemma linear Littlewood-Paley locally modular Lusztig Math Mathematics mild solution minimal structures model theory modular form monster Lie algebra Morley rank Navier-Stokes equations norm 0 vector obtain orthogonal paraproduct algorithm Plancherel measure pointwise proof properties proved relation representation residual root multiplicities satisfies Schwartz class simple roots solutions of Navier-Stokes subalgebra subgroup subspace theorem trivial unipotent unique universal domain uo(x uq(x vertex algebra wavelet analysis wavelet basis Weyl group yields Zariski zeros