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The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the representation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.

Electronic books. -- local. --- Linear algebraic groups. --- Representations of groups. --- Symmetry groups. --- Linear algebraic groups --- Symmetry groups --- Representations of groups --- Mathematical Theory --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Group representation (Mathematics) --- Groups, Representation theory of --- Groups, Symmetry --- Symmetric groups --- Algebraic groups, Linear --- Mathematics. --- Associative rings. --- Rings (Algebra). --- Group theory. --- Nonassociative rings. --- Functions of real variables. --- Combinatorics. --- Group Theory and Generalizations. --- Associative Rings and Algebras. --- Non-associative Rings and Algebras. --- Real Functions. --- Combinatorics --- Mathematical analysis --- Real variables --- Functions of complex variables --- Rings (Algebra) --- Groups, Theory of --- Substitutions (Mathematics) --- Algebraic rings --- Ring theory --- Algebraic fields --- Math --- Science --- Group theory --- Crystallography, Mathematical --- Quantum theory --- Geometry, Algebraic --- Algebraic varieties --- Algebra.

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De Quincey, Thomas

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