On the Hattori-Stallings trace for certain primitive factors of enveloping algebras of semisimple Lie algebras

On the $K$-theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case

“…It follows that Ko(U^,)q is generated by the images of the G-linearized line bundles on X. Finally, as in [21], we show, using the Bernstein trace, that the value of 7^ on these generators is given by a certain polynomial formula. It is hoped that this will bring some information about the isomorphism and Morita equivalence classes of primitive factors.…”

“…I would like to thank Jens Carsten Jantzen, Martin Holland, Rudolf Rentschler and Wolfgang Soergel for useful discussions. I would also like to thank the referee of the article [21], whose illuminating comments greatly simplified my original proof of Proposition 3.1.…”

“…For an arbitrary semisimple Q and a regular weight /^, it was shown in [13], in a special case, and then in [21], in general, that the value of Tu^ on the generators corresponding to (^-linearized line bundles on X was given by WeyPs dimension formula.…”