Representation theory of W-algebras
Representation theory of W-algebras
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DOI：
10.1007/s00222-007-0046-1
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发表时间：
2007-08-01
影响因子：
3.1
通讯作者：
Arakawa, Tomoyuki
中科院分区：
文献类型：
--
作者：
Arakawa, Tomoyuki
研究了与k级棒上的简单李代数（g）相关联的W-代数W-k（（g）over bar）的表示理论。我们证明了“-”约化函子是精确的，并且在任何水平k ∈ C上将不可约模发送到零或不可约模。并且证明了W（k）（g）在bar上的每个不可约最高权表示的特征标完全由（g）在bar上的仿射李代数g的相应不可约最高权表示的特征标决定。从而完成了E. Frenkel，V. Kac和M. Wakimoto关于W-代数的模不变表示的存在性和构造.
We study the representation theory of the W- algebra W-k((g) over bar) associated with a simple Lie algebra (g) over bar at level k. We show that the "-" reduction functor is exact and sends an irreducible module to zero or an irreducible module at any level k epsilon C. Moreover, we show that the character of each irreducible highest weight representation ofW(k)((g) over bar) is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra g of (g) over bar. As a consequence we complete ( for the "-" reduction) the proof of the conjecture of E. Frenkel, V. Kac and M. Wakimoto on the existence and the construction of the modular invariant representations of W- algebras.