Representations of conformal Galilei algebra with integer spin and an application

30th International Colloquium on Group Theoretical Methods in Physics

Aizawa, N.^1 ; Chandrashekar, R.^2 ; Segar, J.^3

Department of Mathematics and Information Sciences, Osaka Prefecture University, Nakamozu Campus, Osaka, Sakai

599-8531, Japan^1

Department of Physics, National Chung Hsing University, Taichung

40227, Taiwan^2

Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai, 600 004, India^3

关键词: Lowest weight modules;    Positive integers;    Semisimple Lie algebras;    Singular vectors;    Two parameter;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012008/pdf
DOI  :  10.1088/1742-6596/597/1/012008

来源: IOP

【 摘 要 】

Conformal Galilei algebra is a class of non-semisimple Lie algebras. Each member of the class is labelled by two parameters d (positive integer) and(positive integer or positive half-integer). We investigate the lowest weight representations of the conformal Galilei algebra for d = 1 and any integer . We start with the Verma modules and then extract all the irreducible lowest weight modules. This is done by searching and explicitly constructing singular vectors. As an application of our construction of singular vectors, we obtain the partial differential equations which are symmetric by kinematical transformation generated by the conformal Galilei algebra.