Generalised Verma modules for the orthosymplectic Lie superalgebra ospk|2

JOURNAL OF ALGEBRA

卷:357

Article

Su, Yucai^1,2  Zhang, R. B.³ 

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Univ Sci & Technol China, Wu Wen Tsun Key Lab Math, Hefei 230026, Peoples R China

[3] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

关键词: Orthosymplectic Lie superalgebras;    Verma modules;    Character formulae;    Cohomology groups;   

DOI  :  10.1016/j.jalgebra.2012.01.026

来源: Elsevier

【 摘 要 】

The composition factors with their multiplicities and the submodule lattices are determined for generalised Verma modules over the orthosymplectic Lie superalgebra osp(k vertical bar 2). The results enable us to obtain explicit formulae for the formal characters and dimensions of the finite-dimensional irreducible modules. Applying these results. we also compute the first and second cohomology groups of the Lie superalgebra with coefficients in finite-dimensional Mac modules and irreducible modules. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free