## Recent Developments in Algebra and Related AreasThis volume contains fifteen articles presented at the International Conference on Algebra and Related Areas held at Tsinghua University, Beijing, in August 2007. Some are surveys and others are research papers on topics including: algebraic geometry, combinatorics, coding theory, Lie algebras, representation theory of finite groups and algebraic groups, and vertex operator algebras, with their applications. This volume is intended for researchers and graduate students in algebra and related areas. |

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### Contents

Preface | 1 |

Minimal Representation Degree of Affine KacMoody | 36 |

A Rationality Problem | 53 |

Copyright | |

9 other sections not shown

### Common terms and phrases

7-design A-module abelian algebraic groups algorithm anti-involution arrow association scheme assume automorphism group Beijing blocks Chevalley group Chinese computation conference graph Corollary defined denote digraph dimension Euclidean designs exists finite fields finite groups formation Galois group geometry GN(A Gr(A graph Grobner basis group G group signature Hamiltonian path Hence highest weight homogeneous elements ideal if-algebra incidence structure inner Galois group integer irreducible isomorphism Lemma Let G Lie algebra linear Math Mathematics matrix minimal mod n2 monomial ordering multi-continued fraction N-gradation nexus nilpotent Noetherian notation Note obtain p-nilpotent p-subgroup polynomial prime problem Proof Proposition prove quasifinite rational respect root system satisfying secret key Section sequence Shum spherical designs strongly regular strongly regular graphs subalgebra subgroup of G subset subspace Sylow subgroup T-filtered T-filtration T-graded Tate pairing Theorem 3.1 theory Ufnarovski vector Verma module vertex Virasoro algebra weight module