Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem write by Jonah Blasiak. This book was released on 2015-04-09. Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem available in PDF, EPUB and Kindle. The Kronecker coefficient is the multiplicity of the -irreducible in the restriction of the -irreducible via the natural map , where are -vector spaces and . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. The authors construct two quantum objects for this problem, which they call the nonstandard quantum group and nonstandard Hecke algebra. They show that the nonstandard quantum group has a compact real form and its representations are completely reducible, that the nonstandard Hecke algebra is semisimple, and that they satisfy an analog of quantum Schur-Weyl duality.
Open Problems in Algebraic Combinatorics
Open Problems in Algebraic Combinatorics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Open Problems in Algebraic Combinatorics write by Christine Berkesch. This book was released on 2024-08-21. Open Problems in Algebraic Combinatorics available in PDF, EPUB and Kindle. In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
Geometry and Complexity Theory
Geometry and Complexity Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry and Complexity Theory write by J. M. Landsberg. This book was released on 2017-09-28. Geometry and Complexity Theory available in PDF, EPUB and Kindle. Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.
Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory
Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory write by Vyjayanthi Chari. This book was released on 2013-11-25. Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory available in PDF, EPUB and Kindle. This volume contains the proceedings of the International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, held August 12-16, 2010, at the National Institute of Advanced Studies, Bangalore, India, and the follow-up conference held May 18-20, 2012, at the University of California, USA. It contains original research and survey articles on various topics in the theory of representations of Lie algebras, quantum groups and algebraic groups, including crystal bases, categorification, toroidal algebras and their generalisations, vertex algebras, Hecke algebras, Kazhdan-Lusztig bases, $q$-Schur algebras, and Weyl algebras.
Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4
Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4 write by Bob Oliver. This book was released on 2016-01-25. Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4 available in PDF, EPUB and Kindle. The author classifies all reduced, indecomposable fusion systems over finite -groups of sectional rank at most . The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional -rank at most . But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.
