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  • Crystal Bases: Representations And Combinatorics

    This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from ... Read more

    $41.99 USD

  • Lie Groups

    by Daniel Bump ...
    Series series Mathematics and Statistics (R0)
    This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has ... Read more

    $62.99 USD

  • Multiple Dirichlet Series, L-functions and Automorphic Forms

    Series series Mathematics and Statistics (R0)
    Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical ... Read more

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  • Weyl Group Multiple Dirichlet Series

    Type A Combinatorial Theory

    Series Book 175 - Annals of Mathematics Studies
    Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be ... Read more

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  • Symmetry: Representation Theory and Its Applications

    In Honor of Nolan R. Wallach

    Series series Mathematics and Statistics (R0)
    Nolan Wallach's mathematical research is remarkable in both its breadth and depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This ... Read more

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  • Classical Finite Transformation Semigroups

    An Introduction

    Series series Mathematics and Statistics (R0)
    The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, ... Read more

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  • Eulerian Numbers

    Series series Mathematics and Statistics (R0)
    This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and ... Read more

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  • A Panorama of Discrepancy Theory

    Series series Mathematics and Statistics (R0)
    This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory.Discrepancy theory concerns ... Read more

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  • Quantum Theory, Groups and Representations

    An Introduction

    by Peter Woit ...
    This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to ... Read more

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  • Quadratic and Higher Degree Forms

    Series series Mathematics and Statistics (R0)
    In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010 ... Read more

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  • Extensions of Positive Definite Functions

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    Series series Mathematics and Statistics (R0)
    This monograph deals with the mathematics of extending given partial data-sets obtained from experiments;Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed ... Read more

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  • Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics

    Series Book 71 - Fields Institute Communications
    This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.Topics presented include:structure and representation theory of reductive algebraic monoidsmonoid schemes and applications of monoidsmonoids related to Lie theoryequivariant embeddings of algebraic groupsconstructions and ... Read more

    $89.09 USD