Representations of Semisimple Lie Algebras in the BGG Category $\mathscr {O}$ (Graduate Studies in Mathematics)

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9780821846780: Representations of Semisimple Lie Algebras in the BGG Category $\mathscr {O}$ (Graduate Studies in Mathematics)

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.

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"One of the goals Humphreys had in mind was to provide a textbook suitable for graduate students. This has been achieved by keeping prerequisites to a minimum, by careful dealing with technical parts of the proofs, and by offering a large number of exercises." ---- Mathematical Reviews

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James E. Humphreys
Editore: American Mathematical Society (2008)
ISBN 10: 0821846787 ISBN 13: 9780821846780
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Descrizione libro American Mathematical Society, 2008. Hardcover. Condizione libro: New. Brand new. We distribute directly for the publisher. 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. Codice libro della libreria 1005120125

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James E. Humphreys
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ISBN 10: 0821846787 ISBN 13: 9780821846780
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Descrizione libro American Mathematical Society, United States, 2008. Hardback. Condizione libro: New. UK ed.. Language: English . Brand New Book. 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. Codice libro della libreria AAN9780821846780

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James E. Humphreys
Editore: American Mathematical Society, United States (2008)
ISBN 10: 0821846787 ISBN 13: 9780821846780
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Descrizione libro American Mathematical Society, United States, 2008. Hardback. Condizione libro: New. UK ed.. Language: English . Brand New Book. 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. Codice libro della libreria AAN9780821846780

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Descrizione libro American Mathematical Society. Hardback. Condizione libro: new. BRAND NEW, Representations of Semisimple Lie Algebras in the BGG Category O, James E. Humphreys, 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. Codice libro della libreria B9780821846780

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Descrizione libro American Mathematical Society, 2008. Hardcover. Condizione libro: New. Codice libro della libreria DADAX0821846787

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Descrizione libro Condizione libro: New. Bookseller Inventory # ST0821846787. Codice libro della libreria ST0821846787

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Descrizione libro American Mathematical Society, 2008. Hardcover. Condizione libro: New. book. Codice libro della libreria 0821846787

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Descrizione libro Amer Mathematical Society, 2008. Hardcover. Condizione libro: Brand New. illustrated edition. 289 pages. 10.30x7.30x0.80 inches. In Stock. Codice libro della libreria __0821846787

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Descrizione libro American Mathematical Society, 2008. Condizione libro: New. Discusses the Kazhdan-Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra $\mathfrak{g}$ over $\mathbb {C}$. This work covers topics including parabolic category $\mathscr {O}$, projective functors, tilting modules, twisting and completion functors and Koszul duality theorem of Beilinson-Ginzburg-Soergel. Series: Graduate Studies in Mathematics. Num Pages: 289 pages, Illustrations. BIC Classification: PBF; PBG. Category: (P) Professional & Vocational. Dimension: 261 x 186 x 21. Weight in Grams: 712. . 2008. Hardcover. . . . . . Codice libro della libreria V9780821846780

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