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Combinatorial Representation Theory

By Ram, Arun

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Book Id: WPLBN0000659516
Format Type: PDF eBook
File Size: 924.88 KB
Reproduction Date: 2005
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Title: Combinatorial Representation Theory  
Author: Ram, Arun
Language: English
Subject: Science., Mathematics, Logic
Publication Date:


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Ram, A. (n.d.). Combinatorial Representation Theory. Retrieved from

Mathematics document containing theorems and formulas.

Table of Contents
24 H EL ENE BARCELO AND ARUN RAM Appendices Contents Introduction 24 Part I 1.What is Combinatorial Representation Theory? 25 What is Representation Theory? 25 Main Questions in Representation Theory 27 Answers Should Be of the Form. . . 29 2.Answers for Sn, the Symmetric Group 30 3.Answers for GL(n; C ), the General Linear Group 34 4.Answers for Finite-Dimensional Complex Semisimple Lie Algebras g 40 Part II 5.Generalizing the Sn Results 42 5.1.The Reflection Groups G(r; p; n) 43 5.2.The \Hecke algebras of reflection groups 44 5.3.Tensor Power Centralizer Algebras 46 5.4. Reflection Groups of Exceptional Type 49 6. Generalizations of GL(n; C ) Results 50 Partial Results for Further Generalizations 50 A1.Basic Representation Theory 52 A2.Partitions and Tableaux 53 A3.The Flag Variety, Unipotent Varieties, and Springer Theory for GL(n; C) 57 A4.Polynomial and Rational Representations of GL(n; C) 59 A5. Schur{Weyl Duality and Young Symmetrizers 60 A6.The Borel{Weil{Bott Construction 61 A7.Complex Semisimple Lie Algebras 62 A8.Roots, Weights and Paths 63 Key words and phrases. Algebraic combinatorics, representations. Barcelo was supported in part by National Science Foundation grant DMS-9510655. Ram was supported in part by National Science Foundation grant DMS-9622985. This paper was written while both authors were in residence at MSRI. We are grateful for the


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