Weight modules of direct limit Lie algebras
Weight modules of direct limit Lie algebras
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直接极限李代数的权模
DOI：
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发表时间：
1998
期刊：
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通讯作者：
I. Penkov
中科院分区：
文献类型：
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作者：
I. Dimitrov;I. Penkov
本文的目的是系统地研究约化李代数的直接极限的不可约权表示，特别是经典的简单直接极限李代数A(∞)、B(∞)、C(∞)和d(∞)的不可约权表示。我们研究任意的，不一定是最高权的不可约重量模，并描述了所有这类模的支撑性。经典直接极限群的表示理论始于G.Olshanskii[O1]，[O2]的开创性工作，现在处于活跃阶段(参见A.Habib[Ha]，L.Natarajan[Na]，K.-H.Neeb[Ne]和L.Natarajan，E.Rodriguez-Carrington和J.A.Wolf[NRW]的最新工作)。然而，直到最近，简单的直接极限李代数的权表示的结构理论还处于初级阶段，因为在书面著作中只讨论了最高权的模(见Yu的著作)。巴赫图林和G.本卡特[BB]，K.-H.Neeb[Ne]，T.D.Palev[P])。我们的方法主要基于最近的文献[DMP]，在文[DMP]中，研究有限维李的权表示的支持度的一般方法。
The purpose of this paper is to initiate a systematic study of the irreducible weight representations of direct limits of reductive Lie algebras and, in particular, of the classical simple direct limit Lie algebras A(∞), B(∞), C(∞), andD(∞). We study arbitrary, not necessarily highest weight, irreducible weight modules and describe the supports of all such modules. The representation theory of the classical direct limit groups has been initiated in the pioneering works of G. Olshanskii [O1], [O2] and is now in an active phase (see the recent works of A. Habib [Ha], L. Natarajan [Na], K.-H. Neeb [Ne], and L. Natarajan, E. Rodriguez-Carrington, and J. A. Wolf [NRW]). Nevertheless, the structure theory of weight representations of the simple direct limit Lie algebras has until recently been still in its infancy as only highest weight modules have been discussed in written works (see the works of Yu. A. Bahturin and G. Benkart [BB], K.-H. Neeb [Ne], and T. D. Palev [P]). Our approach is based mainly on the recent paper [DMP] in which a general method for studying the support of weight representations of finite-dimensional Lie al-