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Extensions of inhomogeneous polynomial representations for sl(m + 1|n)

曹彬涛(中山大学数学与计算科学学院)
2015年03月20日(周五)10:00-11:00  闵行数学楼102报告厅
 
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摘要:We extend an inhomogeneous polynomial representation of special linear
Lie superalgebras sl(m + 1|n) to an inhomogeneous representation on the
tensor space of any irreducible tensor representation of the general linear
Lie superalgebras gl(m|n) with this polynomial space via Shen’s mixed
product. We find a sufficient and necessary condition for irreducibility of
these inhomogeneous representations, and get the Jordan-H¨older series of
those which are not irreducible. Furthermore, we point out that all these
irreducible modules are lowest weight modules. Their lowest weights and
character formulas are obtained.
   
 
 
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