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The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood-Richardson rule and the Schur-Weyl duality. Importantly the authors also present many recent advances in the area, including Lassalle's character formulas, the theory of partition algebras, and an exhaustive exposition of the approach developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises makes this an ideal textbook for graduate students. It will also serve as a useful reference for more experienced researchers across a range of areas, including algebra, computer science, statistical mechanics and theoretical physics.

Symmetry groups. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Quantum theory --- Representations of groups

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This volume gives a detailed and up-to-date overview of the line groups, the groups that describe the symmetry of quasi-one dimensional crystals. Nanotubes, nanowires, nanosprings, nanorods, and polymers are examples remarkable enough to have kept nanoscience as a leading field within material science and solid state physics for more than fifteen years now. The authors present the mathematical foundations, including classifications of the line groups, quasi one-dimensional crystals and quantum numbers, together with important applications. Extensive illustrations related to the physics of nanotubes make the book essential reading in this field above all. The book clearly demonstrates how symmetry is a most profound property of nature and contains valuable results that are published here for the first time.

Group theory --- Nanotubes --- Polymers --- Crystals --- Applied Physics --- Engineering & Applied Sciences --- Nanostructured materials. --- Symmetry groups. --- Groups, Symmetry --- Symmetric groups --- Nanomaterials --- Nanometer materials --- Nanophase materials --- Nanostructure controlled materials --- Nanostructure materials --- Ultra-fine microstructure materials --- Physics. --- Polymers. --- Group theory. --- Crystallography. --- Nanotechnology. --- Theoretical, Mathematical and Computational Physics. --- Polymer Sciences. --- Group Theory and Generalizations. --- Crystallography, Mathematical --- Quantum theory --- Representations of groups --- Microstructure --- Nanotechnology --- Crystallography and Scattering Methods. --- Leptology --- Physical sciences --- Mineralogy --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Polymere --- Polymeride --- Polymers and polymerization --- Macromolecules --- Molecular technology --- Nanoscale technology --- High technology --- Mathematical physics. --- Polymers  . --- Physical mathematics --- Physics --- Mathematics