Combinatorial and Geometric Representation Theory PDF Download

Author: Seok-Jin Kang
Publisher: American Mathematical Soc.
ISBN: 0821832123
Category : Mathematics
Languages : en
Pages : 202

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Book Description
This volume presents the proceedings of the international conference on Combinatorial and Geometric Representation Theory. In the field of representation theory, a wide variety of mathematical ideas are providing new insights, giving powerful methods for understanding the theory, and presenting various applications to other branches of mathematics. Over the past two decades, there have been remarkable developments. This book explains the strong connections between combinatorics, geometry, and representation theory. It is suitable for graduate students and researchers interested in representation theory.

Author: Mahir Bilen Can
Publisher: American Mathematical Society
ISBN: 147047090X
Category : Mathematics
Languages : en
Pages : 218

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Book Description
This volume contains the proceedings of the AMS Special Session on Combinatorial and Geometric Representation Theory, held virtually on November 20–21, 2021. The articles offer an engaging look into recent advancements in geometric representation theory. Despite diverse subject matters, a common thread uniting the articles of this volume is the power of geometric methods. The authors explore the following five contemporary topics in geometric representation theory: equivariant motivic Chern classes; equivariant Hirzebruch classes and equivariant Chern-Schwartz-MacPherson classes of Schubert cells; locally semialgebraic spaces, Nash manifolds, and their superspace counterparts; support varieties of Lie superalgebras; wreath Macdonald polynomials; and equivariant extensions and solutions of the Deligne-Simpson problem. Each article provides a well-structured overview of its topic, highlighting the emerging theories developed by the authors and their colleagues.

Author: V Lakshmibai
Publisher: Springer
ISBN: 9811313938
Category : Mathematics
Languages : en
Pages : 312

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Book Description
This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.

Author: Pramod N. Achar
Publisher: American Mathematical Society
ISBN: 1470471175
Category : Mathematics
Languages : en
Pages : 536

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Book Description
This book is the third Proceedings of the Southeastern Lie Theory Workshop Series covering years 2015–21. During this time five workshops on different aspects of Lie theory were held at North Carolina State University in October 2015; University of Virginia in May 2016; University of Georgia in June 2018; Louisiana State University in May 2019; and College of Charleston in October 2021. Some of the articles by experts in the field describe recent developments while others include new results in categorical, combinatorial, and geometric representation theory of algebraic groups, Lie (super) algebras, and quantum groups, as well as on some related topics. The survey articles will be beneficial to junior researchers. This book will be useful to any researcher working in Lie theory and related areas.

Author: Amritanshu Prasad
Publisher: Cambridge University Press
ISBN: 1316222705
Category : Mathematics
Languages : en
Pages : 206

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Book Description
This book discusses the representation theory of symmetric groups, the theory of symmetric functions and the polynomial representation theory of general linear groups. The first chapter provides a detailed account of necessary representation-theoretic background. An important highlight of this book is an innovative treatment of the Robinson–Schensted–Knuth correspondence and its dual by extending Viennot's geometric ideas. Another unique feature is an exposition of the relationship between these correspondences, the representation theory of symmetric groups and alternating groups and the theory of symmetric functions. Schur algebras are introduced very naturally as algebras of distributions on general linear groups. The treatment of Schur–Weyl duality reveals the directness and simplicity of Schur's original treatment of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.

Author: Francois Bergeron
Publisher: CRC Press
ISBN: 1439865078
Category : Mathematics
Languages : en
Pages : 227

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Book Description
Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and

Author: Filippo Callegaro
Publisher: Springer
ISBN: 3319315803
Category : Mathematics
Languages : en
Pages : 385

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Book Description
This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.

Author: Hélène Barcelo
Publisher: Springer
ISBN: 3030051412
Category : Mathematics
Languages : en
Pages : 362

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Book Description
This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.

Author: Venkatramani Lakshmibai
Publisher: Editions Hermann
ISBN:
Category : Geometry, Algebraic
Languages : en
Pages : 342

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Book Description
Flag varieties constitute an important class of homogeneous spaces. Because of their rich geometry and combinatorics, they represent fundamental objects in the areas of Algebraic Geometry, Algebraic Groups and Representation Theory. This book provides an introduction to the subject, and presents the interplay of flag varieties among Geometry, Combinatorics and Representation Theory. The Schubert subvarieties provide a powerful inductive machinery for the study of flag varieties. The central theme of this book is the theory of Schubert varieties - their geometric properties, ideal theory, singularity theory. This book also presents the relationship between Schubert varieties and certain affine varieties - classical determinantal varieties, ladder determinantal varieties, quiver varieties. varieties of complexes, certain affine toric varieties. This book includes a detailed treatment of the classical determinantal varieties, their normality, Cohen-Macaulayness, singular loci, relationship to classical invariant theory : the treatment uses their relationship to Schubert varieties.

Author: Alexander Soifer
Publisher: Springer Science & Business Media
ISBN: 0387754709
Category : Mathematics
Languages : en
Pages : 292

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Book Description
Geometric Etudes in Combinatorial Mathematics is not only educational, it is inspirational. This distinguished mathematician captivates the young readers, propelling them to search for solutions of life’s problems—problems that previously seemed hopeless. Review from the first edition: The etudes presented here are not simply those of Czerny, but are better compared to the etudes of Chopin, not only technically demanding and addressed to a variety of specific skills, but at the same time possessing an exceptional beauty that characterizes the best of art...Keep this book at hand as you plan your next problem solving seminar. —The American Mathematical Monthly