Generalized projective representations for sl(n+1)

JOURNAL OF ALGEBRA

卷:328

Article

Zhao, Yufeng¹  Xu, Xiaoping² 

[1] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Hua Loo Keng Key Math Lab, Beijing 100190, Peoples R China

关键词: Special linear Lie algebra;    Representation of Lie algebra;    Characteristic identities;   

DOI  :  10.1016/j.jalgebra.2010.07.009

来源: Elsevier

【 摘 要 】

It is well known that n-dimensional projective group gives rise to a non-homogeneous representation of the Lie algebra sl(n + 1) on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known as Larsson functor), we generalize the above representation of sl(n + 1) to a non-homogeneous representation on the tensor space of any finite-dimensional irreducible gl(n)-module with the polynomial space. Moreover, the structure of such a representation is completely determined by employing projection operator techniques and well-known Kostant's characteristic identities for certain matrices with entries in the universal enveloping algebra. In particular, we obtain a new one parameter family of infinite-dimensional irreducible sl(n + 1)-modules. which are in general not highest-weight type, for any given finite-dimensional irreducible sl(n)-module. The results could also be used to study the quantum field theory with the projective group as the symmetry. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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