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Combinatorial and Geometric Representation Theory

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 123/5 ( reviews)

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Book Synopsis Combinatorial and Geometric Representation Theory by : Seok-Jin Kang

Download or read book Combinatorial and Geometric Representation Theory written by Seok-Jin Kang. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Glimpse into Geometric Representation Theory

2024-08-07 Mathematics
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Release : 2024-08-07
Genre : Mathematics
Kind : eBook
Book Rating : 90X/5 ( reviews)

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Book Synopsis A Glimpse into Geometric Representation Theory by : Mahir Bilen Can

Download or read book A Glimpse into Geometric Representation Theory written by Mahir Bilen Can. This book was released on 2024-08-07. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Flag Varieties

2018-06-26 Mathematics
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Release : 2018-06-26
Genre : Mathematics
Kind : eBook
Book Rating : 938/5 ( reviews)

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Book Synopsis Flag Varieties by : V Lakshmibai

Download or read book Flag Varieties written by V Lakshmibai. This book was released on 2018-06-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Categorical, Combinatorial and Geometric Representation Theory and Related Topics

2024-07-11 Mathematics
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Release : 2024-07-11
Genre : Mathematics
Kind : eBook
Book Rating : 175/5 ( reviews)

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Book Synopsis Categorical, Combinatorial and Geometric Representation Theory and Related Topics by : Pramod N. Achar

Download or read book Categorical, Combinatorial and Geometric Representation Theory and Related Topics written by Pramod N. Achar. This book was released on 2024-07-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Combinatorics and Coinvariant Spaces

2009-07-06 Mathematics
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Release : 2009-07-06
Genre : Mathematics
Kind : eBook
Book Rating : 078/5 ( reviews)

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Book Synopsis Algebraic Combinatorics and Coinvariant Spaces by : Francois Bergeron

Download or read book Algebraic Combinatorics and Coinvariant Spaces written by Francois Bergeron. This book was released on 2009-07-06. Available in PDF, EPUB and Kindle. Book excerpt: 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

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