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Author: Kaoru Hiraga
Publisher: American Mathematical Soc.
ISBN: 0821853643
Category : Mathematics
Languages : en
Pages : 110
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Book Description
The theory of $L$-indistinguishability for inner forms of $SL_2$ has been established in the well-known paper of Labesse and Langlands (L-indistinguishability forSL$(2)$. Canad. J. Math. 31 (1979), no. 4, 726-785). In this memoir, the authors study $L$-indistinguishability for inner forms of $SL_n$ for general $n$. Following the idea of Vogan in (The local Langlands conjecture. Representation theory of groups and algebras, 305-379, Contemp. Math. 145 (1993)), they modify the $S$-group and show that such an $S$-group fits well in the theory of endoscopy for inner forms of $SL_n$.
Author: Kaoru Hiraga
Publisher: American Mathematical Soc.
ISBN: 0821853643
Category : Mathematics
Languages : en
Pages : 110
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Book Description
The theory of $L$-indistinguishability for inner forms of $SL_2$ has been established in the well-known paper of Labesse and Langlands (L-indistinguishability forSL$(2)$. Canad. J. Math. 31 (1979), no. 4, 726-785). In this memoir, the authors study $L$-indistinguishability for inner forms of $SL_n$ for general $n$. Following the idea of Vogan in (The local Langlands conjecture. Representation theory of groups and algebras, 305-379, Contemp. Math. 145 (1993)), they modify the $S$-group and show that such an $S$-group fits well in the theory of endoscopy for inner forms of $SL_n$.
Author: Anne-Marie Aubert
Publisher: Springer
ISBN: 9811366284
Category : Mathematics
Languages : en
Pages : 289
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Book Description
This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the enormously influential local Langlands conjectures. The survey gives a precise and accessible formulation of many aspects of the conjectures, highlighting recent refinements, due to the author and her collaborators, and their current status. It also features an extensive account by Colin Bushnell of his work with Henniart on the fine structure of the local Langlands correspondence for general linear groups, beginning with a clear overview of Bushnell–Kutzko’s construction of cuspidal types for such groups. The remaining papers touch on a range of topics in this active area of modern mathematics: group actions on root data, explicit character formulas, classification of discrete series representations, unicity of types, local converse theorems, completions of Hecke algebras, p-adic symmetric spaces. All meet a high level of exposition. The book should be a valuable resource to graduate students and experienced researchers alike.
Author: Werner Ballmann
Publisher: Birkhäuser
ISBN: 3319436481
Category : Mathematics
Languages : en
Pages : 427
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Book Description
This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 22-28. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung.
Author: Mats Boij
Publisher: American Mathematical Soc.
ISBN: 0821869108
Category : Mathematics
Languages : en
Pages : 93
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Book Description
A monomial order ideal is a finite collection X of (monic) monomials such that, whenever M∈X and N divides M, then N∈X. Hence X is a poset, where the partial order is given by divisibility. If all, say t t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h_=(h0=1,h1,...,he), counting the monomials of X in each degree. Equivalently, pure O-sequences can be characterized as the f-vectors of pure multicomplexes, or, in the language of commutative algebra, as the h h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of the early works of Stanley's in this area, and have since played a significant role in at least three different disciplines: the study of simplicial complexes and their f f-vectors, the theory of level algebras, and the theory of matroids. This monograph is intended to be the first systematic study of the theory of pure O-sequences.
Author: Farrell Brumley
Publisher: American Mathematical Soc.
ISBN: 147043573X
Category : Mathematics
Languages : en
Pages : 394
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Book Description
Presents, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers.
Author: Aleksandr Sergeevich Kleshchëv
Publisher: American Mathematical Soc.
ISBN: 0821874314
Category : Mathematics
Languages : en
Pages : 148
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Book Description
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type $A_{p-1}^{(2)}$. The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.
Author: Abdelhamid Meziani
Publisher: American Mathematical Soc.
ISBN: 0821853120
Category : Mathematics
Languages : en
Pages : 90
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Book Description
This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.
Author: Jonathan David Rogawski
Publisher: Princeton University Press
ISBN: 1400882443
Category : Mathematics
Languages : en
Pages : 272
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Book Description
The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.
Author: Tadeusz Iwaniec
Publisher: American Mathematical Soc.
ISBN: 0821853570
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Iwaniec and Onninen (both mathematics, Syracuse U., US) address concrete questions regarding energy minimal deformations of annuli in Rn. One novelty of their approach is that they allow the mappings to slip freely along the boundaries of the domains, where it is most difficult to establish the existence, uniqueness, and invertibility properties of the extremal mappings. At the core of the matter, they say, is the underlying concept of free Lagrangians. After an introduction, they cover in turn principal radial n-harmonics, and the n-harmonic energy. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Author: James Arthur
Publisher: American Mathematical Soc.
ISBN: 0821843664
Category : Mathematics
Languages : en
Pages : 258
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Book Description
"The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at The AMS-IMS-SIAM Joint Summer Research Conference "Representation Theory of Real Reductive Lie Groups" held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature." "This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields."--BOOK JACKET.
