Whittaker 模块的 Kostant 问题

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-01-03 DOI:10.1007/s11005-023-01759-8

Chih-Whi Chen

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引用次数: 0

摘要

我们研究了科斯坦特提出的列支和列支上的维特克模块的经典问题。我们给出了一个充分条件，即对于还原列上的标准维特克模块，科斯坦特问题的答案是肯定的。在同样的条件下，简单维特克模块的正答案被简化为简单最高权模块的正答案。我们提出了几个还原结果，把 I 型列超代上的标准和简单惠特克模块的 Kostant 问题还原为该列超代偶数部分上的相应惠特克模块的问题。

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Kostant’s problem for Whittaker modules

We study the classical problem of Kostant for Whittaker modules over Lie algebras and Lie superalgebras. We give a sufficient condition for a positive answer to Kostant’s problem for the standard Whittaker modules over reductive Lie algebras. Under the same condition, the positivity of the answer for simple Whittaker modules is reduced to that for simple highest weight modules. We develop several reduction results to reduce the Kostant’s problem for standard and simple Whittaker modules over a type I Lie superalgebra to that for the corresponding Whittaker modules over the even part of this Lie superalgebra.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.