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In the past ** Ching Hung Lam** has collaborated on articles with

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AbstractWe study the twisted representations of code vertex operator algebras. For any inner automorphism g of a code VOA MD, we compute the g-twisted modules of MD by using the theory of induced modules. We also show that MD is g-rational if g is an inner automorphism.

AbstractOne would like an explanation of the provocative McKay and Glauberman–Norton observations connecting the extended E8-diagram with pairs of 2A involutions in the Monster sporadic simple group. We propose a down-to-earth model for the 3C-case which exhibits a logic to these connections.

AbstractLet E be an integral lattice. We first discuss some general properties of an SDC lattice, i.e., a sum of two diagonal copies of E in E⊥E. In particular, we show that its group of isometries contains a wreath product. We then specialize this study to the case of E=E8 and provide a new and fairly natural model for those rootless lattices which are sums of a pair of EE8-lattices. This family of lattices was classified in Griess Jr. and Lam (2011) [7]. We prove that this set of isometry types is in bijection with the set of conjugacy classes of rootless elements in the isometry group O(E8), i.e., those h∈O(E8) such that the sublattice (h−1)E8 contains no roots. Finally, our model gives new embeddings of several of these lattices in the Leech lattice.

AbstractIn this paper, we give a coset construction of the orbifold VOA V2A2τ, where τ is an order three automorphism of V2A2. The main idea is to use conjugations of several automorphisms of the lattice VOA VE6, which in some sense are analogous to Frenkel–Lepowsky–Meurman’s triality map. As a consequence, we construct explicitly many intertwining operators among modules of twisted type and obtain lower bounds for their fusion rules.

AbstractIn this paper, a holomorphic vertex operator algebra U of central charge 24 with the weight one Lie algebra A8,3A2,12 is proved to be unique. Moreover, a holomorphic vertex operator algebra of central charge 24 with the weight one Lie algebra F4,6A2,2 is obtained by applying a Z2-orbifold construction to U. The uniqueness of such a vertex operator algebra is also established. By a similar method, we also established the uniqueness of a holomorphic vertex operator algebra of central charge 24 with the weight one Lie algebra E7,3A5,1. As a consequence, we verify that all 71 Lie algebras in Schellekens' list can be realized as the weight one Lie algebras of some holomorphic vertex operator algebras of central charge 24. In addition, we establish the uniqueness of three holomorphic vertex operator algebras of central charge 24 whose weight one Lie algebras have the type A8,3A2,12, F4,6A2,2, and E7,3A5,1.

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