Alexander Kleshchev's Books

Linear and Projective Representations of Symmetric Groups

By: Alexander Kleshchev

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Linear and Projective Representations of Symmetric Groups

By: Alexander Kleshchev

The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own

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Page Count

293

Publisher

Cambridge University Press

Published Date

ISBN 10

1139444069

ISBN 13

9781139444064

Imaginary Schur-Weyl Duality

By: Alexander Kleshchev,Robert Muth

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Imaginary Schur-Weyl Duality

By: Alexander Kleshchev,Robert Muth

The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules—one for each real positive root for the corresponding affine root system X , as well as irreducible imaginary modules—one for each -multiplication. The authors study imaginary modules by means of “imaginary Schur-Weyl duality” and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.

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Page Count

108

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470422492

ISBN 13

9781470422493

Principles of Hydroacoustics

By: Alexander Kleshchev

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Principles of Hydroacoustics

By: Alexander Kleshchev

The textbook “Principles of Hydroacoustics” is devoted to the study of the equations of liquid and solid elastic (isotropic and anisotropic). The textbook provides the main characteristics of the reflectivity of ideal and elastic bodies as the simple forms (sphere, infinite cylinder, prolate and oblate spheroids) and bodies of non-analytical shape (finite cylinder with hemispheres at the ends). Moreover, in the textbook, along with classical methods of diffraction theory, such numerical methods as the finite element method and the boundary element method are used. The textbook also studies the theory of synthesis of hydroacoustic antennas and criteria for acoustic diffraction measurements in a hydroacoustic basin.

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209

Publisher

Cambridge Scholars Publishing

Published Date

ISBN 10

1036404544

ISBN 13

9781036404543

Diffraction, Radiation and Propagation of Elastic Waves in Isotropic and Anisotropic Bodies

By: Alexander Kleshchev

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Diffraction, Radiation and Propagation of Elastic Waves in Isotropic and Anisotropic Bodies

By: Alexander Kleshchev

This book presents the main results of extensive research on diffraction, radiation and propagation of elastic waves. In recent years, there has been an increase in interest in problems in the fields of diffraction, radiation and propagation of elastic waves associated with the interaction of bodies both with each other and with media interfaces. In addition, there is currently extensive focus on the solution of three-dimensional wave problems, with the help of Debye potentials, for elastic isotropic and anisotropic bodies of analytical and non-analytical forms.

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122

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Cambridge Scholars Publishing

Published Date

ISBN 10

152754141X

ISBN 13

9781527541412

Yangians and Classical Lie Algebras

By: Alexander Molev

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Yangians and Classical Lie Algebras

By: Alexander Molev

The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. This book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.

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Page Count

422

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821843745

ISBN 13

9780821843741

Linear and Projective Representations of Symmetric Groups

By: Alexander Kleshchev

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Linear and Projective Representations of Symmetric Groups

By: Alexander Kleshchev

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293

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Cambridge University Press

Published Date

ISBN 10

1139444069

ISBN 13

9781139444064

Fixed Point Theorems for Plane Continua with Applications

By: Alexander M. Blokh,Robbert J. Fokkink,John C. Mayer,Lex G. Oversteegen,E. D. Tymchatyn

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Fixed Point Theorems for Plane Continua with Applications

By: Alexander M. Blokh,Robbert J. Fokkink,John C. Mayer,Lex G. Oversteegen,E. D. Tymchatyn

In this memoir the authors present proofs of basic results, including those developed so far by Harold Bell, for the plane fixed point problem: Does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by Bell but without accessible proofs. The authors define the concept of the variation of a map on a simple closed curve and relate it to the index of the map on that curve: Index = Variation + 1. A prime end theory is developed through hyperbolic chords in maximal round balls contained in the complement of a non-separating plane continuum $X$. They define the concept of an outchannel for a fixed point free map which carries the boundary of $X$ minimally into itself and prove that such a map has a unique outchannel, and that outchannel must have variation $-1$. Also Bell's Linchpin Theorem for a foliation of a simply connected domain, by closed convex subsets, is extended to arbitrary domains in the sphere. The authors introduce the notion of an oriented map of the plane and show that the perfect oriented maps of the plane coincide with confluent (that is composition of monotone and open) perfect maps of the plane. A fixed point theorem for positively oriented, perfect maps of the plane is obtained. This generalizes results announced by Bell in 1982.

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Page Count

117

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821884883

ISBN 13

9780821884881

Stalin's Commandos

Ukrainian Partisan Forces on the Eastern Front

By: Alexander Gogun

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Stalin's Commandos

Ukrainian Partisan Forces on the Eastern Front

By: Alexander Gogun

At the height of World War II, a large number of Soviet partisans fought on the Eastern Front against the Axis occupation. In this book, Alexander Gogun looks at the forces operating in Ukraine. The Nazi atrocities were often matched by partisan brutality. The author examines the indiscriminate use of scorched-earth tactics by the partisans, the destruction of their own villages, partisan-generated Nazi reprisals against civilians, and the daily incidents of robbery, drunkenness, rape and bloody internal conflicts that were reported to be widespread amongst the red partisans. Gogun also analyses allegations of the use of bacteriological weapons and even instances of cannibalism. He shows that all these practices were not a product of the culture of warfare nor a spontaneous 'people's response' to the unremitting brutality of Nazi rule but a specific feature of Stalin's total war strategy.

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Page Count

350

Publisher

Bloomsbury Publishing

Published Date

ISBN 10

085772438X

ISBN 13

9780857724380

The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

By: Georgia Benkart,Thomas Bradford Gregory,Alexander Premet

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The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

By: Georgia Benkart,Thomas Bradford Gregory,Alexander Premet

Volume 197, number 920 (second of 5 numbers).

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Page Count

164

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842269

ISBN 13

9780821842263

Sugawara Operators for Classical Lie Algebras

By: Alexander Molev:

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Sugawara Operators for Classical Lie Algebras

By: Alexander Molev:

The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical -algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical -algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.

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Page Count

321

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470436590

ISBN 13

9781470436599

Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

By: Sergey Zelik,Alexander Mielke

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Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

By: Sergey Zelik,Alexander Mielke

The authors study semilinear parabolic systems on the full space ${\mathbb R}^n$ that admit a family of exponentially decaying pulse-like steady states obtained via translations. The multi-pulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. They prove a global center-manifold reduction theorem for the temporal evolution of such multi-pulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, The authors verify the existence of Sinai-Bunimovich space-time chaos in 1D space-time periodically forced Swift-Hohenberg equation.

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112

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842641

ISBN 13

9780821842645

Characters of Groups and Lattices over Orders

From Ordinary to Integral Representation Theory

By: Alexander Zimmermann

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Characters of Groups and Lattices over Orders

From Ordinary to Integral Representation Theory

By: Alexander Zimmermann

This is the fi rst textbook leading coherently from classical character theory to the theory of lattices over orders and integral representations of fi nite groups. Character theory is developed in a highly pedagogical way including many examples and exercises covering at once the fi rst defi nitions up to Clifford theory, Brauer’s induction theorem and the splitting fi eld theorem, as well as self-dual simple modules allowing bilinear forms. This latter part is done step by step using the approach given by Sin and Willems. Dirichlet characters and Dirichlet’s result on primes in arithmetic progressions are given as an application. Examples of integral representations of fi nite groups are already detailed at a quite early stage where appropriate, so that the more systematic treatment of lattices over orders is natural. After that, the necessary number theory and homological algebra is developed as far as needed. Maximal as well as hereditary orders are introduced and the Auslander- Buchsbaum theorem is proved. The Jordan-Zassenhaus theorem on the fi niteness of lattices in a given vector space is fully proved. Then the development and properties of class groups of orders is a fi rst focus. As a further highlight Swan’s example of a stably free but not free ideal over the integral group ring of the generalised quaternion group of order 32 is developed in great detail. A student friendly introduction to ordinary representation theory Many examples and exercises, including solutions for some of them, make the book well suited for self-study Leads coherently from ordinary character theory to the integral representation theory of lattices over orders Several topics appear for the fi rst time in a textbook, such as Sin-Willems’ approach to self-dual simple modules and Swan‘s example of a stably free non free ideal.

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Page Count

363

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

311070255X

ISBN 13

9783110702552

Diffraction, Radiation and Propagation of Elastic Waves in Isotropic and Anisotropic Bodies

By: Alexander Kleshchev

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Diffraction, Radiation and Propagation of Elastic Waves in Isotropic and Anisotropic Bodies

By: Alexander Kleshchev

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122

Publisher

Cambridge Scholars Publishing

Published Date

ISBN 10

1527539938

ISBN 13

9781527539938

Principles of Hydroacoustics

By: Alexander Kleshchev

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Principles of Hydroacoustics

By: Alexander Kleshchev

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Page Count

209

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Cambridge Scholars Publishing

Published Date

ISBN 10

1036404544

ISBN 13

9781036404543

Book's by Alexander Kleshchev

Linear and Projective Representations of Symmetric Groups

Linear and Projective Representations of Symmetric Groups

Imaginary Schur-Weyl Duality

Imaginary Schur-Weyl Duality

Principles of Hydroacoustics

Principles of Hydroacoustics

Diffraction, Radiation and Propagation of Elastic Waves in Isotropic and Anisotropic Bodies

Diffraction, Radiation and Propagation of Elastic Waves in Isotropic and Anisotropic Bodies

Yangians and Classical Lie Algebras

Yangians and Classical Lie Algebras

Linear and Projective Representations of Symmetric Groups

Linear and Projective Representations of Symmetric Groups

Fixed Point Theorems for Plane Continua with Applications

Fixed Point Theorems for Plane Continua with Applications

Stalin's Commandos

Stalin's Commandos

The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

Sugawara Operators for Classical Lie Algebras

Sugawara Operators for Classical Lie Algebras

Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

Characters of Groups and Lattices over Orders

Characters of Groups and Lattices over Orders

Diffraction, Radiation and Propagation of Elastic Waves in Isotropic and Anisotropic Bodies

Diffraction, Radiation and Propagation of Elastic Waves in Isotropic and Anisotropic Bodies

Principles of Hydroacoustics

Principles of Hydroacoustics

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