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Title of Journal: Invent math

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Abbravation: Inventiones mathematicae

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Springer-Verlag

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10.1007/bf03035122

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1432-1297

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Representation theory of mathcalWalgebras

Authors: Tomoyuki Arakawa
Publish Date: 2007/03/30
Volume: 169, Issue: 2, Pages: 219-320
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Abstract

We study the representation theory of the mathcalWalgebra mathcalW kbarmathfrakg associated with a simple Lie algebra barmathfrakg 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∈ℂ Moreover we show that the character of each irreducible highest weight representation of mathcalW kbarmathfrakg is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra mathfrakg of barmathfrakg 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 mathcalWalgebras

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Other Papers In This Journal:
  1. Serre’s modularity conjecture (I)
  2. Serre’s modularity conjecture (I)
  3. Erratum to: Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space
  4. Image of Λ -adic Galois representations modulo p
  5. The Kodaira dimension of the moduli of K3 surfaces
  6. Brownian Gibbs property for Airy line ensembles
  7. Degree formula for connective K -theory
  8. Some quantitative results in $${\mathcal {C}}^0$$ symplectic geometry
  9. Convexes divisibles IV : Structure du bord en dimension 3
  10. The classification of irreducible admissible mod p representations of a p -adic GL n
  11. Some prime factorization results for type II 1 factors
  12. $\mathcal{C}^{2}$ surface diffeomorphisms have symbolic extensions
  13. On the weights of mod p Hilbert modular forms
  14. Operator-algebraic superridigity for SL n (ℤ), n ≥3
  15. Exceptional zero formulae and a conjecture of Perrin-Riou
  16. F-singularities of pairs and Inversion of Adjunction of arbitrary codimension
  17. Knot homology via derived categories of coherent sheaves II, $\mathfrak{sl}_{m}$ case
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