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Order, Lattices, Representation Theory
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e-books in this category
Introduction to Representations of Real Semisimple Lie Groups
by Matvei Libine - arXiv , 2012
These are lecture notes for a one semester introductory course I gave at Indiana University. The goal was to make this exposition as clear and elementary as possible. A particular emphasis is given on examples involving SU(1,1).
Symplectic Reflection Algebras
by Gwyn Bellamy - arXiv , 2012
The emphasis throughout is on examples to illustrate the many different facets of symplectic reflection algebras. Exercises are included at the end of each lecture in order for the student to get a better feel for these algebras.
Lectures on Representations of Complex Semi-Simple Lie Groups
by Thomas J. Enright - Tata Institute of Fundamental Research , 1981
The purpose of these lectures is to describe a factorial correspondence between the theory of admissible representations for a complex semisimple Lie group and the theory of highest weight modules for a semisimple Lie algebra.
Lectures on Some Aspects of p-Adic Analysis
by F. Bruhat - Tata Institute of Fundamental Research , 1963
The text covers the classical theory of valuated fields, results about representations of classical groups over a locally compact valuated field, and Dwork's proof of the rationality of the zeta function of an algebraic variety over a finite field.
Lectures on Lie Groups and Representations of Locally Compact Groups
by F. Bruhat - Tata Institute of Fundamental Research , 1958
We consider some heterogeneous topics relating to Lie groups and the general theory of representations of locally compact groups. We have rigidly adhered to the analytic approach in establishing the relations between Lie groups and Lie algebras.
Representation Theory of Compact Groups
by Michael Ruzhansky, Ville Turunen - Aalto TKK , 2008
Contents: Groups (Groups without topology, Group actions and representations); Topological groups (Compact groups, Haar measure, Fourier transforms on compact groups..); Linear Lie groups (Exponential map, Lie groups and Lie algebras); Hopf algebras.
Group Representation Theory
by Kevin McGerty - Imperial College , 2010
Topics: elementary group theory; examples of groups; conjugacy classes; Cayleys theorem; representations of groups; Maschke's theorem, Schur's lemma; representations of abelian groups; the character of a group representation; the group algebra; etc.
Finite Group Representations for the Pure Mathematician
by Peter Webb - University of Minnesota , 2007
The book is intended to be used as a learning tool by people who do not know the subject. It is intended to be appropriate for non-specialists in the area of representation theory, such as those whose primary interest is topology or combinatorics.
Lectures on Representation Theory and Invariant Theory
by William Crawley-Boevey - University of Leeds , 1990
These are lectures on the symmetric group, the general linear group and invariant theory. The course covered as much of the classical theory as time allowed. The text requires some knowledge of rings and modules, character theory, affine varieties.
Representations of Reductive p-adic Groups
by Fiona Murnaghan - University of Toronto , 2009
Contents: Valuations and local fields; Smooth representations of locally compact totally disconnected groups; Haar measure, convolution, and characters of admissible representations; Induced representations - general properties; etc.
Introduction to Representation Theory
by Fiona Murnaghan - University of Toronto , 2010
Contents: Representation Theory of Groups - Algebraic Foundations; Representations of Finite Groups; Representations of SL2(Fq); Representations of Finite Groups of Lie Type; Topological Groups, Representations, and Haar Measure; etc.
Groups: Presentations and Representations
by Christopher Cooper - Macquarie University , 2008
This is a first course on group theory suitable to a third year student. It motivates group theory with many illustrative examples such as shuffling of cards and permutation puzzles. There's an elementary introduction to representation theory.
An Elementary Introduction to Groups and Representations
by Brian C. Hall - arXiv , 2000
An elementary introduction to Lie groups, Lie algebras, and their representations. Topics include definitions and examples of Lie groups and Lie algebras, the basics of representations theory, the Baker-Campbell-Hausdorff formula, and more.
Introduction to Representation Theory
by Pavel Etingof, at al. - MIT , 2009
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.
Varieties of Lattices
by Peter Jipsen, Henry Rose - Springer , 1992
Presents the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The text includes preliminaries that make the material accessible to anyone with basic knowledge of universal algebra.