Equivariant Fredholm modules for the full quantum flag manifold of

  • Christian Voigt

    School of Mathematics (1) Université Clermont Auvergne and Statistics Université Blaise Pascal University of Glasgow Laboratoire de Mathématiques 15 University Gardens BP 10448 Glasgow G12 8QW F-63000 Clermont-Ferrand United Kingdom France (2) CNRS, UMR 6620, LM F-63178 Aubiere France Robert.Yuncken
  • Robert Yuncken

    School of Mathematics (1) Université Clermont Auvergne and Statistics Université Blaise Pascal University of Glasgow Laboratoire de Mathématiques 15 University Gardens BP 10448 Glasgow G12 8QW F-63000 Clermont-Ferrand United Kingdom France (2) CNRS, UMR 6620, LM F-63178 Aubiere France Robert.Yuncken
Equivariant Fredholm modules for the full quantum flag manifold of $\mathrm{SU}_q(3)$ cover
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Abstract

We introduce -algebras associated to the foliation structure of a quantum flag manifold. We use these to construct -equivariant Fredholm modules for the full quantum flag manifold of , based on an analytical version of the Bernstein-Gelfand-Gelfand complex. As a consequence we deduce that the flag manifold satisfies Poincaré duality in equivariant -theory. Moreover, we show that the Baum-Connes conjecture with trivial coefficients holds for the discrete quantum group dual to .

Cite this article

Christian Voigt, Robert Yuncken, Equivariant Fredholm modules for the full quantum flag manifold of . Doc. Math. 20 (2015), pp. 433–490

DOI 10.4171/DM/495