Geodesic
Equivariant Fredholm modules for the full quantum flag manifold of $\mathrm{SU}_q(3)$
Documenta mathematica, Tome 20 (2015), pp. 433-490
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We introduce C∗-algebras associated to the foliation structure of a quantum flag manifold. We use these to construct SLq​(3,C)-equivariant Fredholm modules for the full quantum flag manifold Xq​=SUq​(3)/T of SUq​(3), based on an analytical version of the Bernstein-Gelfand-Gelfand complex. As a consequence we deduce that the flag manifold Xq​ satisfies Poincaré duality in equivariant KK-theory. Moreover, we show that the Baum-Connes conjecture with trivial coefficients holds for the discrete quantum group dual to SUq​(3).
DOI : 10.4171/dm/495
Classification : 19K35, 20G42, 46L80
Mots-clés : quantum groups, Poincaré duality, noncommutative geometry, baum-connes conjecture, quantum flag manifolds, Bernstein-Gelfand-Gelfand complex, kasparov theory 
@article{10_4171_dm_495,
     author = {Christian Voigt and Robert Yuncken},
     title = {Equivariant {Fredholm} modules for the full quantum flag manifold of $\mathrm{SU}_q(3)$},
     journal = {Documenta mathematica},
     pages = {433--490},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/495},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/495/}
}
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Christian Voigt; Robert Yuncken. Equivariant Fredholm modules for the full quantum flag manifold of $\mathrm{SU}_q(3)$. Documenta mathematica, Tome 20 (2015), pp. 433-490. doi: 10.4171/dm/495

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