Alessandro Carotenuto
Convex orderings on positive roots and quantum tangent spaces
In noncommutative differential geometry the information on the differential structure of a noncommutative space is encapsulated in the choice of a first order differential calculus. In the case of quantum homogeneous spaces, this is equivalent to giving the choice of a so-called quantum tangent space. In a recent work of Ó Buachalla and Somberg, it was proposed that quantum tangent spaces for quantum flag manifolds can be derived from the theory of PBW basis of quantized enveloping algebras defined by Lusztig. This depends in turn on the choice of a reduced decomposition of the longest element $w_0$ of the Weyl group. In this talk, based on a collaboration with C. Hohlweg and P. Papi, I will show the combinatorial conditions under which a reduced decomposition of $w_0$ gives rise to a quantum tangent space.
