INVARIANTS OF THE HALF-LIBERATED ORTHOGONAL GROUP

By T. Banica, Roland Vergnioux. 2009

56 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/db6616c0f7cb765151a9f988f5a42c916c6916e8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quantum Isometries and Noncommutative Spheres (2009, methodology): “A second piece of evidence comes from the results in [ 7 ], which suggest that the free quantum groups might be actually supergroups.”
De Finetti theorems for easy quantum groups (2009, background): “Since the complex Gaussian distribution is known to be characterized by unitary invariance, this appears to be closely related to the connection between Un and O∗ n observed in [5, 8].”