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Article Dans Une Revue Annales de l'Institut Fourier Année : 2011

Invariants of the half-liberated orthogonal group

Résumé

The half-liberated orthogonal group $O_n^*$ appears as intermediate quantum group between the orthogonal group $O_n$, and its free version $O_n^+$. We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between $O_n^*$ and $U_n$, a non abelian discrete group playing the role of weight lattice for $O_n^*$, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that the discrete quantum group dual to $O_n^*$ has polynomial growth.

Dates et versions

hal-00562702 , version 1 (03-02-2011)

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Teodor Banica, Roland Vergnioux. Invariants of the half-liberated orthogonal group. Annales de l'Institut Fourier, 2011, 60 (6), pp.2137-2164. ⟨hal-00562702⟩
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