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Author | : Erhard Neher |
Publisher | : American Mathematical Soc. |
Total Pages | : 226 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 082185237X |
Download Geometric Representation Theory and Extended Affine Lie Algebras Book in PDF, ePub and Kindle
Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.
Author | : Erhard Neher |
Publisher | : American Mathematical Soc. |
Total Pages | : 213 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9780821871614 |
Download Geometric Representation Theory and Extended Affine Lie Algebras Book in PDF, ePub and Kindle
This text presents lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the developments in Lie algebras and representation theory in the last two decades.
Author | : Karl-Hermann Neeb |
Publisher | : Springer Science & Business Media |
Total Pages | : 492 |
Release | : 2010-10-17 |
Genre | : Mathematics |
ISBN | : 0817647414 |
Download Developments and Trends in Infinite-Dimensional Lie Theory Book in PDF, ePub and Kindle
This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
Author | : Philippe Gille |
Publisher | : American Mathematical Soc. |
Total Pages | : 124 |
Release | : 2013-10-23 |
Genre | : Mathematics |
ISBN | : 0821887742 |
Download Torsors, Reductive Group Schemes and Extended Affine Lie Algebras Book in PDF, ePub and Kindle
The authors give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that the authors take draws heavily from the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows the authors to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.
Author | : Yun Gao |
Publisher | : American Mathematical Soc. |
Total Pages | : 314 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821845071 |
Download Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications Book in PDF, ePub and Kindle
This volume contains the proceedings of the conference on Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, which was held at the Banff International Research Station, Banff, Canada, from March 2-7, 2008. Many of the papers include new results on different aspects of quantum affine algebras, extended affine Lie algebras, and their applications in other areas of mathematics and physics. Any reader interested in learning about the recent developments in quantum affine algebras and extended affine Lie algebras will benefit from this book.
Author | : Vlastimil Dlab |
Publisher | : American Mathematical Soc. |
Total Pages | : 502 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821834169 |
Download Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry Book in PDF, ePub and Kindle
These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ``instructional'' workshop preceding the conference, there were also workshops on ``Commutative Algebra, Algebraic Geometry and Representation Theory'', ``Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ``Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Author | : Yun Gao, Naihuan Jing, Michael Lau, and Kailash C. Misra |
Publisher | : American Mathematical Soc. |
Total Pages | : 314 |
Release | : 2010 |
Genre | : Geometry, Affine |
ISBN | : 0821858327 |
Download Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications Book in PDF, ePub and Kindle
Author | : A. Broer |
Publisher | : Springer Science & Business Media |
Total Pages | : 455 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401591318 |
Download Representation Theories and Algebraic Geometry Book in PDF, ePub and Kindle
The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.
Author | : Neil Chriss |
Publisher | : Springer Science & Business Media |
Total Pages | : 506 |
Release | : 2009-12-24 |
Genre | : Mathematics |
ISBN | : 0817649387 |
Download Representation Theory and Complex Geometry Book in PDF, ePub and Kindle
"The book is largely self-contained...There is a nice introduction to symplectic geometry and a charming exposition of equivariant K-theory. Both are enlivened by examples related to groups...An attractive feature is the attempt to convey some informal ‘wisdom’ rather than only the precise definitions. As a number of results [are] due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory...it has already proved successful in introducing a new generation to the subject." (Bulletin of the AMS)
Author | : Sam Kass |
Publisher | : Univ of California Press |
Total Pages | : 312 |
Release | : 1990-01-01 |
Genre | : Science |
ISBN | : 9780520067684 |
Download Affine Lie Algebras, Weight Multiplicities, and Branching Rules Book in PDF, ePub and Kindle
00 This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference. This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference.