QUANTIZATION OF COMPACT SYMMETRIC SPACES: TWO APPROACHES

I will explain two ways of quantizing compact symmetric spaces. The first is due to Letzter and Kolb, giving explicit generators of the dual coideal. The second is essentially due to Enriquez and Etingof, and relies on cyclotomic Knizhnik-Zamolodchikov equations. Both approaches make sense in the formal and analytic (0<q<1) settings. They are equivalent in a suitable sense for the sphere, therefore giving two ways of looking at Podleś spheres. In the formal setting, we can now show that they are equivalent in general. (Joint work with Kenny De Commer, Lars Tuset and Makoto Yamashita.)