Combinatorial And Geometric Representation Theory

Author : Seok-Jin Kang,Kyu-Hwan Lee
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 53,8 Mb
Release : 2003
Category : Combinatorial analysis
ISBN : 9780821832127

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Combinatorial and Geometric Representation Theory by Seok-Jin Kang,Kyu-Hwan Lee Pdf

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 : Pramod N. Achar,Kailash C. Misra,Daniel Ken Nakano
Publisher : Unknown
Page : 0 pages
File Size : 53,8 Mb
Release : 2024
Category : Group theory
ISBN : 1470471175

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Categorical, Combinatorial and Geometric Representation Theory and Related Topics by Pramod N. Achar,Kailash C. Misra,Daniel Ken Nakano Pdf

Author : Mahir Can,Jörg Feldvoss
Publisher : Unknown
Page : 0 pages
File Size : 42,7 Mb
Release : 2024
Category : Combinatorial analysis
ISBN : 147047090X

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A Glimpse Into Geometric Representation Theory by Mahir Can,Jörg Feldvoss Pdf

Author : V. Lakshmibai,Justin Brown
Publisher : Springer
Page : 172 pages
File Size : 52,9 Mb
Release : 2015-09-25
Category : Mathematics
ISBN : 9781493930821

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The Grassmannian Variety by V. Lakshmibai,Justin Brown Pdf

This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

Author : V Lakshmibai,Justin Brown
Publisher : Springer
Page : 312 pages
File Size : 50,9 Mb
Release : 2018-06-26
Category : Mathematics
ISBN : 9789811313936

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Flag Varieties by V Lakshmibai,Justin Brown Pdf

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 : Filippo Callegaro,Frederick Cohen,Corrado De Concini,Eva Maria Feichtner,Giovanni Gaiffi,Mario Salvetti
Publisher : Springer
Page : 379 pages
File Size : 48,5 Mb
Release : 2016-08-27
Category : Mathematics
ISBN : 9783319315805

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Configuration Spaces by Filippo Callegaro,Frederick Cohen,Corrado De Concini,Eva Maria Feichtner,Giovanni Gaiffi,Mario Salvetti Pdf

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 : Naihuan Jing
Publisher : World Scientific
Page : 172 pages
File Size : 47,7 Mb
Release : 2003-06-27
Category : Science
ISBN : 9789814485500

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Algebraic Combinatorics and Quantum Groups by Naihuan Jing Pdf

Algebraic combinatorics has evolved into one of the most active areas of mathematics during the last several decades. Its recent developments have become more interactive with not only its traditional field representation theory but also algebraic geometry, harmonic analysis and mathematical physics. This book presents articles from some of the key contributors in the area. It covers Hecke algebras, Hall algebras, the Macdonald polynomial and its deviations, and their relations with other fields. Contents:Uno's Conjecture on Representation Types of Hecke Algebras (S Ariki)Quiver Varieties, Afine Lie Algebras, Algebras of BPS States, and Semicanonical Basis (I Frenkel et al.)Divided Differences of Type D and the Grassmannian of Complex Structures (H Duan & P Pragacz)Tableaux Statistics For Two Part Macdonald Polynomials (L Lapointe & J Morse)A Crystal to Rigged Configuration Bijection for Nonexceptional Affine Algebras (M Okado et al.)Littlewood's Formulas for Characters of Orthogonal and Symplectic Groups (A Lascoux)A q-Analog of Schur's Q-Functions (G Tudose & M Zabrocki) Readership: Researchers and graduate students in algebraic combinatorics, representation theory and quantum groups. Keywords:Algebras;Representation Theory;Polynomid;Varities;Q-Functions

Author : Emily H. Moore,Harriet Suzanne Katcher Pollatsek
Publisher : American Mathematical Soc.
Page : 315 pages
File Size : 54,5 Mb
Release : 2013-06-13
Category : Mathematics
ISBN : 9780821891766

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Difference Sets by Emily H. Moore,Harriet Suzanne Katcher Pollatsek Pdf

Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of f

Author : Stuart Margolis,Franco Saliola,Benjamin Steinberg
Publisher : American Mathematical Society
Page : 135 pages
File Size : 52,9 Mb
Release : 2021-12-30
Category : Mathematics
ISBN : 9781470450427

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Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry by Stuart Margolis,Franco Saliola,Benjamin Steinberg Pdf

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Author : Andrew J. Duncan,N. D. Gilbert,James Howie
Publisher : Cambridge University Press
Page : 340 pages
File Size : 50,6 Mb
Release : 1995
Category : Mathematics
ISBN : 0521465958

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Combinatorial and Geometric Group Theory, Edinburgh 1993 by Andrew J. Duncan,N. D. Gilbert,James Howie Pdf

Authoritative collection of surveys and papers that will be indispensable to all research workers in the area.

Author : Jianxun Hu,Changzheng Li,Leonardo C. Mihalcea
Publisher : Springer Nature
Page : 367 pages
File Size : 48,6 Mb
Release : 2020-10-24
Category : Mathematics
ISBN : 9789811574511

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Schubert Calculus and Its Applications in Combinatorics and Representation Theory by Jianxun Hu,Changzheng Li,Leonardo C. Mihalcea Pdf

This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6–10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.

Author : Bruno Benedetti,Emanuele Delucchi,Luca Moci
Publisher : Springer
Page : 227 pages
File Size : 50,8 Mb
Release : 2015-10-31
Category : Mathematics
ISBN : 9783319201559

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Combinatorial Methods in Topology and Algebra by Bruno Benedetti,Emanuele Delucchi,Luca Moci Pdf

Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.

Author : Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 46,9 Mb
Release : 2011-01-28
Category : Mathematics
ISBN : 9783764399115

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Combinatorial and Geometric Group Theory by Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura Pdf

This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.

Author : Hélène Barcelo,Gizem Karaali,Rosa Orellana
Publisher : Springer
Page : 362 pages
File Size : 44,9 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9783030051419

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Recent Trends in Algebraic Combinatorics by Hélène Barcelo,Gizem Karaali,Rosa Orellana Pdf

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 : Amritanshu Prasad
Publisher : Cambridge University Press
Page : 205 pages
File Size : 44,7 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9781107082052

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Representation Theory by Amritanshu Prasad Pdf

This book examines the fundamental results of modern combinatorial representation theory. The exercises are interspersed with text to reinforce readers' understanding 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.