## A Recursive Formula for Characters of Simple Lie Algebras |

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### Contents

Known results | 12 |

Generalizing the known results the main theorem | 20 |

Corollaries and applications | 33 |

2 other sections not shown

### Common terms and phrases

A2 and B2 Antoine and Speiser c^eN Cartan subalgebra characteristic function coefficient complex simple Lie computation Corollary 4.9 definition dim V(X distinct positive roots distinct weights Doctor of Philosophy dominant weights due to Kostant element weW elements of Q equals the number Equation evaluating both sides Figure fixed following lemma FORMULA FOR CHARACTERS fundamental weights gefl geometric highest weight i-0 wew i=l Proof irreducible module Killing form known character formulae Let XeA+ module Z(X multiplicative inverse mx(y N(m+l,l N(m+l,n+l non-simple positive roots non-simple roots notation number of distinct nx(v obtain oooo prove Theorems 2.5 RECURSIVE FORMULA set of weights sgn(w sgn(w)p sides of Theorem SIMPLE LIE ALGEBRAS simple roots Steven Neil Kass subset sum of distinct sum of positive Sums of non-simple tensor product term corresponding thesis unique veA+ Verma module w(X+6)-6 is dominant Weight lattice weights of V(X Weyl group action Weyl's formula write written