Download specht modules over a hecke alg of the symm group an explicit resolution of the specht module over a hecke algebra of the symmetric group in pdf or read specht modules over a hecke alg of the symm group an explicit resolution of the specht module over a hecke algebra of the symmetric group in pdf online books in PDF, EPUB and Mobi Format. Click Download or Read Online button to get specht modules over a hecke alg of the symm group an explicit resolution of the specht module over a hecke algebra of the symmetric group in pdf book now. This site is like a library, Use search box in the widget to get ebook that you want.



Finite Dimensional Algebras And Quantum Groups

Author: Bangming Deng
Publisher: American Mathematical Soc.
ISBN: 0821841866
Size: 66.66 MB
Format: PDF
View: 1679
Download and Read
The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak {gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature.

Geometric Complexity Theory Iv Nonstandard Quantum Group For The Kronecker Problem

Author: Jonah Blasiak
Publisher: American Mathematical Soc.
ISBN: 1470410117
Size: 14.62 MB
Format: PDF, Docs
View: 5853
Download and Read
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.

Linear Algebraic Monoids

Author: Lex Renner
Publisher: Springer Science & Business Media
ISBN: 3540275568
Size: 57.21 MB
Format: PDF, Kindle
View: 6843
Download and Read
This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.

The Symmetric Group

Author: Bruce Sagan
Publisher: Springer Science & Business Media
ISBN: 1475768044
Size: 71.19 MB
Format: PDF, Docs
View: 927
Download and Read
This book brings together many of the important results in this field. From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." --ZENTRALBLATT MATH

Handbook Of Tilting Theory

Author: Dieter Happel
Publisher: Cambridge University Press
ISBN: 9780521680455
Size: 34.69 MB
Format: PDF, ePub, Docs
View: 6025
Download and Read
A handbook of key articles providing both an introduction and reference for newcomers and experts alike.

Hecke Algebras With Unequal Parameters

Author: George Lusztig
Publisher: American Mathematical Soc.
ISBN: 0821833561
Size: 62.50 MB
Format: PDF, Kindle
View: 4417
Download and Read
Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over $p$-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties.In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives researchers and graduate students working in the theory of algebraic groups and their representations an invaluable insight and a wealth of new and useful information.

Blocks Of Tame Representation Type And Related Algebras

Author: K. Erdmann
Publisher: Springer
ISBN: 3540471154
Size: 27.70 MB
Format: PDF, ePub, Docs
View: 306
Download and Read
This monograph studies algebras that are associated to blocks of tame representation type. Over the past few years, a range of new results have been obtained and a comprehensive account of these is provided here to- gether with some new proofs of known results. Some general theory of algebras is also presented, as a means of understanding the subject. The book is addressed to researchers and graduate students interested in the links between representations of finite-dimensional algebras and modular group representation theory. The basic properties of modules and finite-dimensional algebras are assumed known.

Introduction To Quantum Groups

Author: George Lusztig
Publisher: Springer Science & Business Media
ISBN: 9780817647179
Size: 39.94 MB
Format: PDF, Mobi
View: 2882
Download and Read
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

Lectures On Algebraic Categorification

Author: Volodymyr Mazorchuk
Publisher: European Mathematical Society
ISBN: 9783037191088
Size: 44.24 MB
Format: PDF, ePub, Mobi
View: 1490
Download and Read
The term "categorification" was introduced by Louis Crane in 1995 and refers to the process of replacing set-theoretic notions by the corresponding category-theoretic analogues. This text mostly concentrates on algebraical aspects of the theory, presented in the historical perspective, but also contains several topological applications, in particular, an algebraic (or, more precisely, representation-theoretical) approach to categorification. It consists of fifteen sections corresponding to fifteen one-hour lectures given during a Master Class at Aarhus University, Denmark in October 2010. There are some exercises collected at the end of the text and a rather extensive list of references. Video recordings of all (but one) lectures are available from the Master Class website. The book provides an introductory overview of the subject rather than a fully detailed monograph. The emphasis is made on definitions, examples and formulations of the results. Most proofs are either briefly outlined or omitted. However, complete proofs can be found by tracking references. It is assumed that the reader is familiar with the basics of category theory, representation theory, topology, and Lie algebra.

Classical Fourier Analysis

Author: Loukas Grafakos
Publisher: Springer
ISBN: 1493911945
Size: 20.83 MB
Format: PDF
View: 5391
Download and Read
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references.