A family of representations of the Lie superalgebra (gl(1 vertical bar l-1))over-cap(C-q)

作者：Bhargava Sandeep; Chen Hongjia; Gao Yun^*

来源：Journal of Algebra, 2013, 386: 61-76.

DOI：10.1016/j.jalgebra.2013.03.025

• Lie superalgebra
• Representation
• Root graded Lie superalgebra

We construct an action of the Lie superalgebras <((gl(1 vertical bar l-1)))over cap>(C-q) involving one parameter mu on the exterior algebra with infinitely many variables and show this representation to be irreducible if and only if mu, is nonzero. We also discuss the module structure and irreducibility over a Lie subsuperalgebra graded by the root system A(1, l - 1).

• 出版日期2013-7-15
• 单位中国科学技术大学