On homogeneous vector bundles
- 作者：Indranil Biswas ; S. Subramanian
- 关键词：Homogeneous space ; Vector bundle ; Stability
- 刊名：Bulletin des Sciences Mathematiques
- 出版年：2008
- 期刊代码：7_00074497
- 类别：mt
- 出版时间：July-August 2008
- 卷：132
- 期：5
- 页码：419-424
- 文件大小：95 K
摘要
Let G be a simply connected linear algebraic group, defined over the field of complex numbers, whose Lie algebra is simple. Let P be a proper parabolic subgroup of G. Let E be a holomorphic vector bundle over ration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6VKR-4S0JN2Y-1&_mathId=mml1&_user=1067359&_cdi=6129&_rdoc=5&_acct=C000058823&_version=1&_userid=2795313&md5=486953cedc60776cf093ade44b1d948e" title="Click to view the MathML source" alt="Click to view the MathML source">G/P such that E admits a homogeneous structure. Assume that E is not stable. Then E admits a homogeneous structure with the following property: There is a nonzero subbundle ration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6VKR-4S0JN2Y-1&_mathId=mml2&_user=1067359&_cdi=6129&_rdoc=5&_acct=C000058823&_version=1&_userid=2795313&md5=cc5d4906227585d27e6adce1a881150c" title="Click to view the MathML source" alt="Click to view the MathML source">F
E left invariant by the action of G such that ration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6VKR-4S0JN2Y-1&_mathId=mml3&_user=1067359&_cdi=6129&_rdoc=5&_acct=C000058823&_version=1&_userid=2795313&md5=9c098f461173ca2727bbbb73412ac0e1" title="Click to view the MathML source" alt="Click to view the MathML source">degree(F)/rank(F)
degree(E)/rank(E).
E left invariant by the action of G such that ration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6VKR-4S0JN2Y-1&_mathId=mml3&_user=1067359&_cdi=6129&_rdoc=5&_acct=C000058823&_version=1&_userid=2795313&md5=9c098f461173ca2727bbbb73412ac0e1" title="Click to view the MathML source" alt="Click to view the MathML source">degree(F)/rank(F)degree(E)/rank(E).