Harish-Chandra homomorphisms for p-adic groups
Author(s)
Bibliographic Information
Harish-Chandra homomorphisms for p-adic groups
（Regional conference series in mathematics, no. 59）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c1985
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Note
On t.p. the German (Fraktur) lower case "p" is used in "p-adic" in the title
"Supported by the National Science Foundation."
"Expository lectures from the CBMS regional conference held at the University of Chicago, August 8-12, 1983"--T.p. verso
Bibliography: p. 75-76
Description and Table of Contents
Description
This book introduces a systematic new approach to the construction and analysis of semi simple $p$-adic groups. The basic construction presented here provides an analogue in certain cases of the Harish-Chandra homomorphism, which has played an essential role in the theory of semi simple Lie groups. The book begins with an overview of the representation theory of GL$_n$ over finite groups.The author then explicitly establishes isomorphisms between certain convolution algebras of functions on two different groups. Because of the form of the isomorphisms, basic properties of representations are preserved, thus giving a concrete example to the correspondences predicted by the general philosphy of Langlands. The first chapter, suitable as an introduction for graduate students, requires only a basic knowledge of representation theory of finite groups and some familiarity with the general linear group and the symmetric group. The later chapters introduce researchers in the field to a new method for the explicit construction and analysis of representations of $p$-adic groups, a powerful method clearly capable of extensive further development.
Table of Contents
A Hecke algebra approach to the representations of GL$_n(F_q)$ Hecke algebras for GL$_n$ over local fields: introduction Harish-Chandra homomorphism in the unramified anisotropic case.
by "Nielsen BookData"