The purpose of the present note is to prove that the parabolic inductions of the orbit datum and Dixmier algebras can be induced by stages. And as an appliction, we have proved that for SO(2n+1, C), SP(2n, C), F\-4 an...The purpose of the present note is to prove that the parabolic inductions of the orbit datum and Dixmier algebras can be induced by stages. And as an appliction, we have proved that for SO(2n+1, C), SP(2n, C), F\-4 and G\-2, the inductions of complete prime Abel orbit datum are independent of the Choice of parabolic subgroups.展开更多
David Vogan gave programmatic conjectures about the Dixmier's map and he made two conjectures that induction may be independent of the choice of parabolic group used and the sheets of orbit data are conjugated or ...David Vogan gave programmatic conjectures about the Dixmier's map and he made two conjectures that induction may be independent of the choice of parabolic group used and the sheets of orbit data are conjugated or disjointed[1]. In our previous paper, we gave a geometric version of the parabolic induction of the geometric orbit datum (i.e. orbit covers), and proved Vogan's first conjecture for geometric orbit datum:the parabolic induction of the geometric orbit datum is independent of the choice of parabolic group. In this paper, we will prove the other Vogan's conjecture, that is, the sheets are conjugated or disjointed for classical semisimple complex groups.展开更多
We study a family of ＂symmetric＂ multiparameter quantized Weyl alge- bras A-q,A n（K） and some related algebras. We compute the Nakayama automorphism of A-q,A n（K）, give a necessary and sufficient condition for A...We study a family of ＂symmetric＂ multiparameter quantized Weyl alge- bras A-q,A n（K） and some related algebras. We compute the Nakayama automorphism of A-q,A n（K）, give a necessary and sufficient condition for A-q,A n（K） to be Calabi-Yau, and prove that A-q,A n（K） is cancellative. We study the automorphisms and isomorphism problem for A-q,A n（K） and .A-q,A n（K[t]）. Similar results are established for the Maltsiniotis multiparam- eter quantized Weyl algebraA-q,A n（K） and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization （A-q,A n（K））z and determine its automorphism group.展开更多
Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometr...Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.展开更多
文摘The purpose of the present note is to prove that the parabolic inductions of the orbit datum and Dixmier algebras can be induced by stages. And as an appliction, we have proved that for SO(2n+1, C), SP(2n, C), F\-4 and G\-2, the inductions of complete prime Abel orbit datum are independent of the Choice of parabolic subgroups.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 19731040 & 10171048).
文摘David Vogan gave programmatic conjectures about the Dixmier's map and he made two conjectures that induction may be independent of the choice of parabolic group used and the sheets of orbit data are conjugated or disjointed[1]. In our previous paper, we gave a geometric version of the parabolic induction of the geometric orbit datum (i.e. orbit covers), and proved Vogan's first conjecture for geometric orbit datum:the parabolic induction of the geometric orbit datum is independent of the choice of parabolic group. In this paper, we will prove the other Vogan's conjecture, that is, the sheets are conjugated or disjointed for classical semisimple complex groups.
文摘We study a family of ＂symmetric＂ multiparameter quantized Weyl alge- bras A-q,A n（K） and some related algebras. We compute the Nakayama automorphism of A-q,A n（K）, give a necessary and sufficient condition for A-q,A n（K） to be Calabi-Yau, and prove that A-q,A n（K） is cancellative. We study the automorphisms and isomorphism problem for A-q,A n（K） and .A-q,A n（K[t]）. Similar results are established for the Maltsiniotis multiparam- eter quantized Weyl algebraA-q,A n（K） and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization （A-q,A n（K））z and determine its automorphism group.
基金the National Natural Science Foundation of China (Grant No. 19731040)
文摘Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.
