Imaginary Schur Weyl Duality
Download Imaginary Schur Weyl Duality full books in PDF, epub, and Kindle. Read online free Imaginary Schur Weyl Duality ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: Alexander Kleshchev |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 108 |
Release |
: 2017-01-18 |
ISBN-10 |
: 9781470422493 |
ISBN-13 |
: 1470422492 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Imaginary Schur-Weyl Duality by : Alexander Kleshchev
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.
Author |
: Pavel I. Etingof |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 240 |
Release |
: 2011 |
ISBN-10 |
: 9780821853511 |
ISBN-13 |
: 0821853511 |
Rating |
: 4/5 (11 Downloads) |
Synopsis Introduction to Representation Theory by : Pavel I. Etingof
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Author |
: V Lakshmibai |
Publisher |
: Springer |
Total Pages |
: 315 |
Release |
: 2018-06-26 |
ISBN-10 |
: 9789811313936 |
ISBN-13 |
: 9811313938 |
Rating |
: 4/5 (36 Downloads) |
Synopsis Flag Varieties by : V Lakshmibai
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 |
: Caroline Gruson |
Publisher |
: Springer |
Total Pages |
: 231 |
Release |
: 2018-10-23 |
ISBN-10 |
: 9783319982717 |
ISBN-13 |
: 3319982710 |
Rating |
: 4/5 (17 Downloads) |
Synopsis A Journey Through Representation Theory by : Caroline Gruson
This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.
Author |
: H. Hofer |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 230 |
Release |
: 2017-07-13 |
ISBN-10 |
: 9781470422035 |
ISBN-13 |
: 1470422034 |
Rating |
: 4/5 (35 Downloads) |
Synopsis Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory by : H. Hofer
In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyfold theory the authors use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.
Author |
: Ben Webster |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 154 |
Release |
: 2018-01-16 |
ISBN-10 |
: 9781470426507 |
ISBN-13 |
: 1470426501 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Knot Invariants and Higher Representation Theory by : Ben Webster
The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for sl and sl and by Mazorchuk-Stroppel and Sussan for sl . The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is sl , the author shows that these categories agree with certain subcategories of parabolic category for gl .
Author |
: Akinari Hoshi |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 228 |
Release |
: 2017-07-13 |
ISBN-10 |
: 9781470424091 |
ISBN-13 |
: 1470424096 |
Rating |
: 4/5 (91 Downloads) |
Synopsis Rationality Problem for Algebraic Tori by : Akinari Hoshi
The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank and is given. The authors show that there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension , and there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension . The authors make a procedure to compute a flabby resolution of a -lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a -lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby -lattices of rank up to and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for -lattices holds when the rank , and fails when the rank is ...
Author |
: Mikhail Ershov |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 148 |
Release |
: 2017-09-25 |
ISBN-10 |
: 9781470426040 |
ISBN-13 |
: 1470426048 |
Rating |
: 4/5 (40 Downloads) |
Synopsis Property ($T$) for Groups Graded by Root Systems by : Mikhail Ershov
The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.
Author |
: A. M. Mason |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 106 |
Release |
: 2018-02-23 |
ISBN-10 |
: 9781470426859 |
ISBN-13 |
: 1470426854 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Orthogonal and Symplectic $n$-level Densities by : A. M. Mason
In this paper the authors apply to the zeros of families of -functions with orthogonal or symplectic symmetry the method that Conrey and Snaith (Correlations of eigenvalues and Riemann zeros, 2008) used to calculate the -correlation of the zeros of the Riemann zeta function. This method uses the Ratios Conjectures (Conrey, Farmer, and Zimbauer, 2008) for averages of ratios of zeta or -functions. Katz and Sarnak (Zeroes of zeta functions and symmetry, 1999) conjecture that the zero statistics of families of -functions have an underlying symmetry relating to one of the classical compact groups , and . Here the authors complete the work already done with (Conrey and Snaith, Correlations of eigenvalues and Riemann zeros, 2008) to show how new methods for calculating the -level densities of eigenangles of random orthogonal or symplectic matrices can be used to create explicit conjectures for the -level densities of zeros of -functions with orthogonal or symplectic symmetry, including all the lower order terms. They show how the method used here results in formulae that are easily modified when the test function used has a restricted range of support, and this will facilitate comparison with rigorous number theoretic -level density results.
Author |
: Igor Burban |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 134 |
Release |
: 2017-07-13 |
ISBN-10 |
: 9781470425371 |
ISBN-13 |
: 1470425378 |
Rating |
: 4/5 (71 Downloads) |
Synopsis Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems by : Igor Burban
In this article the authors develop a new method to deal with maximal Cohen–Macaulay modules over non–isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen–Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen–Macaulay representation type. The authors' approach is illustrated on the case of k as well as several other rings. This study of maximal Cohen–Macaulay modules over non–isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.