I have several questions about Steinberg group and K2 for symplectic group:


1. Can I extend the definition of Steinberg symbols to symplectic case? Will they generate the center of Steinberg group?
2. Does the center of symplectic Steinberg group coincide with K2 (the kernel of $\mathrm{SpSt}\rightarrow\mathrm{Sp}$ as usual)?
3. Is there an analogue for Matsumoto's theorem?


I tryed to read "Sur les sous-groupes arithmetiques des groupes semi-simples deployes" by Hideya Matsumoto and all I got to know about symplectic case is that there is some problems with long roots in Cl. Also, is it written in english anywhere about non-Al K-theory? There is "The Classical groups and K-theory" by Hahn and O'Meara, but it tells about SL and about unitary groups only.



Symplectic Steinberg group
There is useful information about the symplectic analogues of the Steinberg group, the Steinberg symbols, and the $K\_2$ functor in some of Michael Stein's papers from the '70's. In particular, see his papers "Generators, relations and coverings of Chevalley groups over commutative rings" and "Surjective stability in dimension $0$ for $K\_{2}$ and related functors" and "Injective stability for $K\_{2}$ of local rings".


