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Article Dans Une Revue The Michigan Mathematical Journal Année : 2013

The space of generalised G2-theta functions of level one

Résumé

Let C be a smooth projective complex curve of genus at least 2. For a simply-connected complex Lie group G the vector space of global sections H^0(M(G), L^l) of the l-th power of the ample generator L of the Picard group of the moduli stack of principal G-bundles over C is commonly called the space of generalized G-theta functions or Verlinde space of level l. In the case G = G_2, the exceptional Lie group of automorphisms of the complex Cayley algebra, we study natural linear maps between the Verlinde space H^0(M(G_2), L) of level one and some Verlinde spaces for SL_2 and SL_3. We deduce that the image of the monodromy representation of the WZW-connection for G = G_2 and l=1 is infinite.

Dates et versions

hal-00759974 , version 1 (03-12-2012)

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Citer

Chloé Grégoire, Christian Pauly. The space of generalised G2-theta functions of level one. The Michigan Mathematical Journal, 2013, pp.857-867. ⟨hal-00759974⟩
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