Stability In Modules For Classical Lie Algebras
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Stability in Modules for Classical Lie Algebras
Author | : Georgia Benkart,Daniel J. Britten,Frank W. Lemire |
Publsiher | : American Mathematical Soc. |
Total Pages | : 165 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 9780821824924 |
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During the last century, mathematicians and physicists alike have studied extensively the finite dimensional irreducible representations of complex classical Lie algebras. These studies have led to numerous formulas for computing the dimensions, weights, weight multiplicities, and tensor products of the representations. The dependence of these quantities on the rank of the Lie algebra has been revealed in recent investigations using Schur functions and characters.
Stability in Modules for Classical Lie Superalgebras
Author | : Chanyoung Lee |
Publsiher | : Unknown |
Total Pages | : 248 |
Release | : 1992 |
Genre | : Electronic Book |
ISBN | : WISC:89046262994 |
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Yangians and Classical Lie Algebras
Author | : Alexander Molev |
Publsiher | : American Mathematical Soc. |
Total Pages | : 422 |
Release | : 2007 |
Genre | : Lie algebras |
ISBN | : 9780821843741 |
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The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. This book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.
Classical Lie Algebras at Infinity
Author | : Ivan Penkov,Crystal Hoyt |
Publsiher | : Springer Nature |
Total Pages | : 245 |
Release | : 2022-01-05 |
Genre | : Mathematics |
ISBN | : 9783030896607 |
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Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Projective Modules over Lie Algebras of Cartan Type
Author | : Daniel Ken Nakano |
Publsiher | : American Mathematical Soc. |
Total Pages | : 84 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 9780821825303 |
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This monograph focuses on extending theorems for the classical Lie algebras in order to determine the structure and representation theory for Lie algebras of Cartan type. More specifically, Nakano investigates the block theory for the restricted universal enveloping algebras of the Lie algebras of Cartan type. The first section employs techniques developed by Holmes and Nakano to prove a Brauer-Humphreys reciprocity law for graded restricted Lie algebras and also to find the decompositions for the intermediate (Verma) modules used in the reciprocity law. The second section uses this information to investigate the structure of projective modules for the Lie algebras of types W and K. The restricted enveloping algebras for these Lie algebras are shown to have one block. Furthermore, Nakano provides a procedure for computing the Cartan invariants for Lie algebras of types W and K, given knowledge about the decomposition of the generalized Verma modules and about the Jantzen matrix of the classical/reductive zero component. Noteworthy for its readability and the continuity of its theme and purpose, this monograph appeals to graduate students and researchers interested in Lie algebras.
Lie Algebras and Their Representations
Author | : Seok-Jin Kang,Symposium on Lie Algebras,Myung-Hwan Kim,Insok Lee |
Publsiher | : American Mathematical Soc. |
Total Pages | : 242 |
Release | : 1996 |
Genre | : Lie algebras |
ISBN | : 9780821805121 |
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Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.
Representations and Invariants of the Classical Groups
Author | : Roe Goodman,Nolan R. Wallach |
Publsiher | : Cambridge University Press |
Total Pages | : 708 |
Release | : 2000-01-13 |
Genre | : Mathematics |
ISBN | : 0521663482 |
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More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.
Lie Algebras Graded by the Root Systems BC r r geq 2
Author | : Bruce Normansell Allison,Georgia Benkart,Yun Gao |
Publsiher | : American Mathematical Soc. |
Total Pages | : 158 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780821828113 |
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Introduction The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra, $r\ge 3$ (excluding type $\mathrm{D}_3)$ Models for $\mathrm{BC}_r$-graded Lie algebras, $r\ge 3$ (excluding type $\mathrm{D}_3)$ The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Central extensions, derivations and invariant forms Models of $\mathrm{BC}_r$-graded Lie algebras with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Appendix: Peirce decompositions in structurable algebras References.