## The Mathematical Legacy of Harish-Chandra: A Celebration of Representation Theory and Harmonic Analysis : an AMS Special Session Honoring the Memory of Harish-Chandra, January 9-10, 1998, Baltimore, Maryland (Google eBook)Harish-Chandra, Robert S. Doran, V. S. Varadarajan Harish-Chandra was a mathematician of great power, vision, and remarkable ingenuity. His profound contributions to the representation theory of Lie groups, harmonic analysis, and related areas left researchers a rich legacy that continues today. This book presents the proceedings of an AMS Special Session entitled, "Representation Theory and Noncommutative Harmonic Analysis: A Special Session Honoring the Memory of Harish-Chandra", which marked 75 years since his birth and 15 years since his untimely death at age 60. Contributions to the volume were written by an outstanding group of internationally known mathematicians. Included are expository and historical surveys and original research papers. The book also includes talks given at the IAS Memorial Service in 1983 by colleagues who knew Harish-Chandra well. Also reprinted are two articles entitled, "Some Recollections of Harish-Chandra", by A. Borel, and "Harish-Chandra's c-Function: A Mathematical Jewel", by S. Helgason. In addition, an expository paper, "An Elementary Introduction to Harish-Chandra's Work", gives an overview of some of his most basic mathematical ideas with references for further study. This volume offers a comprehensive retrospective of Harish-Chandra's professional life and work. Personal recollections give the book particular significance. Readers should have an advanced-level background in the representation theory of Lie groups and harmonic analysis. |

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### Contents

1 | |

Some Recollections of HarishChandra | 35 |

G DANIEL MOSTOW | 51 |

Stabilization of a Family of Differential Equations | 77 |

Orbital Integrals of Nilpotent Orbits | 97 |

A View from | 111 |

Bruhat Filtrations and Whittaker Vectors for Real Groups | 151 |

Germs Characters and the Fourier Transforms | 191 |

HarishChandras cFunction A Mathematical Jewel | 273 |

HarishChandra Homomorphisms | 321 |

S Varadarajan | 331 |

Intertwining Operators and Small Unitary Representations | 403 |

On Some Problems in Analysis Suggested by Representation | 433 |

Distributional Reciprocity and Generalized Gelfand Pairs | 471 |

Germs of Characters of Admissible Representations | 501 |

SeibergWitten Equations on Locally Symmetric Spaces | 517 |

Bessel Functions on Boundary Orbits and Singular | 223 |

Restriction of Small Discrete Series Representations | 255 |

### Common terms and phrases

abelian admissible representation assume automorphism Cartan subgroup class function cohomology compact subgroup complex conjecture conjugate contains convex COROLLARY corresponding coset decomposition define denote differential operators direct sum discrete series characters discrete series representations distributions element equivalent finite dimensional follows Fourier transform Gelfand pair geodesic group G Haar measure Harish Harish-Chandra harmonic analysis Hecke algebra Hence Hermitian highest weight Hilbert space holomorphic discrete series homogeneous spaces homology induced infinitesimal character invariant involution irreducible admissible representation irreducible representation isomorphism Iwahori kernel Lemma Let G Lie algebra linear Math Mathematics matrix maximal module multiplicity noncompact notation orbital integrals orthogonal p-adic groups parabolic subalgebra parabolic subgroup Plancherel formula positive roots PROOF Proposition reductive groups representation of G representation theory representation TT restriction result semigroup semisimple Lie groups simple roots subgroup of G subset subspace supercuspidal representations Suppose symmetric spaces two-structure unipotent unitary representations vector Weyl group