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Derived Langlands: Monomial Resolutions Of Admissible Representations (Hardcover)
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Derived Langlands: Monomial Resolutions Of Admissible Representations (Hardcover)
Series: Series on Number Theory and Its Applications, 15
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Total price: R3,286
Discovery Miles: 32 860
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The Langlands Programme is one of the most important areas in
modern pure mathematics. The importance of this volume lies in its
potential to recast many aspects of the programme in an entirely
new context. For example, the morphisms in the monomial category of
a locally p-adic Lie group have a distributional description, due
to Bruhat in his thesis. Admissible representations in the
programme are often treated via convolution algebras of
distributions and representations of Hecke algebras. The monomial
embedding, introduced in this book, elegantly fits together these
two uses of distribution theory. The author follows up this
application by giving the monomial category treatment of the
Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.This
book gives a new categorical setting in which to approach
well-known topics. Therefore, the context used to explain examples
is often the more generally accessible case of representations of
finite general linear groups. For example, Galois base-change and
epsilon factors for locally p-adic Lie groups are illustrated by
the analogous Shintani descent and Kondo-Gauss sums, respectively.
General linear groups of local fields are emphasized. However,
since the philosophy of this book is essentially that of homotopy
theory and algebraic topology, it includes a short appendix showing
how the buildings of Bruhat-Tits, sufficient for the general linear
group, may be generalised to the tom Dieck spaces (now known as the
Baum-Connes spaces) when G is a locally p-adic Lie group.The
purpose of this monograph is to describe a functorial embedding of
the category of admissible k-representations of a locally profinite
topological group G into the derived category of the additive
category of the admissible k-monomial module category. Experts in
the Langlands Programme may be interested to learn that when G is a
locally p-adic Lie group, the monomial category is closely related
to the category of topological modules over a sort of enlarged
Hecke algebra with generators corresponding to characters on
compact open modulo the centre subgroups of G. Having set up this
functorial embedding, how the ingredients of the celebrated
Langlands Programme adapt to the context of the derived monomial
module category is examined. These include automorphic
representations, epsilon factors and L-functions, modular forms,
Weil-Deligne representations, Galois base change and Hecke
operators.
General
Imprint: |
World Scientific Publishing Co Pte Ltd
|
Country of origin: |
Singapore |
Series: |
Series on Number Theory and Its Applications, 15 |
Release date: |
2019 |
First published: |
2019 |
Authors: |
Victor P. Snaith
|
Dimensions: |
161 x 236 x 24mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
356 |
ISBN-13: |
978-981-3275-74-4 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
Groups & group theory
|
LSN: |
981-3275-74-X |
Barcode: |
9789813275744 |
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