Representations Of Semisimple Lie Algebras In The Bgg Category Mathscr O
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Representations Of Semisimple Lie Algebras In The Bgg Category Mathscr O
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Author : James E. Humphreys
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Representations Of Semisimple Lie Algebras In The Bgg Category Mathscr O written by James E. Humphreys and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This is the first textbook treatment of work leading to the landmark 1979 Kazhdan-Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra $\mathfrak{g}$ over $\mathbb {C}$. The setting is the module category $\mathscr {O}$ introduced by Bernstein-Gelfand-Gelfand, which includes all highest weight modules for $\mathfrak{g}$ such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of $\mathfrak{g}$. Basic techniques in category $\mathscr {O}$ such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan-Lusztig Conjecture (due to Beilinson-Bernstein and Brylinski-Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: $D$-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category $\mathscr {O}$, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson-Ginzburg-Soergel.
Representations Of Semisimple Lie Algebras In The Bgg Category O
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Author : James E. Humphreys
language : en
Publisher: American Mathematical Soc.
Release Date :
Representations Of Semisimple Lie Algebras In The Bgg Category O written by James E. Humphreys and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This is the first textbook treatment of work leading to the landmark 1979 Kazhdan-Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra $\mathfrak{g}$ over $\mathbb {C}$. The setting is the module category $\mathscr {O}$ introduced by Bernstein-Gelfand-Gelfand, which includes all highest weight modules for $\mathfrak{g}$ such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of $\mathfrak{g}$. Basic techniques in category $\mathscr {O}$ such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan-Lusztig Conjecture (due to Beilinson-Bernstein and Brylinski-Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: $D$-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category $\mathscr {O}$, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson-Ginzburg-Soergel.
Moduli Spaces And Vector Bundles
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Author : Steve Bradlow
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-21
Moduli Spaces And Vector Bundles written by Steve Bradlow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-21 with Mathematics categories.
Coverage includes foundational material as well as current research, authored by top specialists within their fields.
The Symmetric Group
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Author : Bruce E. Sagan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Symmetric Group written by Bruce E. Sagan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
I have been very gratified by the response to the first edition, which has resulted in it being sold out. This put some pressure on me to come out with a second edition and now, finally, here it is. The original text has stayed much the same, the major change being in the treatment of the hook formula which is now based on the beautiful Novelli-Pak-Stoyanovskii bijection (NPS 97]. I have also added a chapter on applications of the material from the first edition. This includes Stanley's theory of differential posets (Stn 88, Stn 90] and Fomin's related concept of growths (Fom 86, Fom 94, Fom 95], which extends some of the combinatorics of Sn-representations. Next come a couple of sections showing how groups acting on posets give rise to interesting representations that can be used to prove unimodality results (Stn 82]. Finally, we discuss Stanley's symmetric function analogue of the chromatic polynomial of a graph (Stn 95, Stn ta]. I would like to thank all the people, too numerous to mention, who pointed out typos in the first edition. My computer has been severely reprimanded for making them. Thanks also go to Christian Krattenthaler, Tom Roby, and Richard Stanley, all of whom read portions of the new material and gave me their comments. Finally, I would like to give my heartfelt thanks to my editor at Springer, Ina Lindemann, who has been very supportive and helpful through various difficult times.
Thermodynamics And An Introduction To Thermostatistics
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Author : Herbert B. Callen
language : en
Publisher: John Wiley & Sons
Release Date : 1991-01-16
Thermodynamics And An Introduction To Thermostatistics written by Herbert B. Callen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-16 with Science categories.
The only text to cover both thermodynamic and statistical mechanics--allowing students to fully master thermodynamics at the macroscopic level. Presents essential ideas on critical phenomena developed over the last decade in simple, qualitative terms. This new edition maintains the simple structure of the first and puts new emphasis on pedagogical considerations. Thermostatistics is incorporated into the text without eclipsing macroscopic thermodynamics, and is integrated into the conceptual framework of physical theory.
Combinatorics Of Coxeter Groups
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Author : Anders Bjorner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-25
Combinatorics Of Coxeter Groups written by Anders Bjorner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-25 with Mathematics categories.
Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups
An Introduction To Mechanics
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Author : Daniel Kleppner
language : en
Publisher:
Release Date : 1981
An Introduction To Mechanics written by Daniel Kleppner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Complex Semisimple Lie Algebras
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Author : Jean-Pierre Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Complex Semisimple Lie Algebras written by Jean-Pierre Serre and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
These notes are a record of a course given in Algiers from lOth to 21st May, 1965. Their contents are as follows. The first two chapters are a summary, without proofs, of the general properties of nilpotent, solvable, and semisimple Lie algebras. These are well-known results, for which the reader can refer to, for example, Chapter I of Bourbaki or my Harvard notes. The theory of complex semisimple algebras occupies Chapters III and IV. The proofs of the main theorems are essentially complete; however, I have also found it useful to mention some complementary results without proof. These are indicated by an asterisk, and the proofs can be found in Bourbaki, Groupes et Algebres de Lie, Paris, Hermann, 1960-1975, Chapters IV-VIII. A final chapter shows, without proof, how to pass from Lie algebras to Lie groups (complex-and also compact). It is just an introduction, aimed at guiding the reader towards the topology of Lie groups and the theory of algebraic groups. I am happy to thank MM. Pierre Gigord and Daniel Lehmann, who wrote up a first draft of these notes, and also Mlle. Franr,:oise Pecha who was responsible for the typing of the manuscript.
Lectures On Real Semisimple Lie Algebras And Their Representations
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Author : A. L. Onishchik
language : en
Publisher: European Mathematical Society
Release Date : 2004
Lectures On Real Semisimple Lie Algebras And Their Representations written by A. L. Onishchik and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The book begins with a simplified (and somewhat extended and corrected) exposition of the main results of F. Karpelevich's 1955 paper and relates them to the theory of Cartan-Iwahori. It concludes with some tables, where an involution of the Dynkin diagram that allows for finding self-conjugate representations is described and explicit formulas for the index are given. In a short addendum, written by J. V. Silhan, this involution is interpreted in terms of the Satake diagram.
Semi Simple Lie Algebras And Their Representations
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Author : Robert N. Cahn
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1984
Semi Simple Lie Algebras And Their Representations written by Robert N. Cahn and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.