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періодичних видань НАН України
Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras
Інший ID:
2010 Mathematics Subject Classification: 17B10; 58J70
DOI:10.3842/SIGMA.2015.002
DOI:10.3842/SIGMA.2015.002
Посилання:
Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras / N. Aizawa, R. Chandrashekar, J. Segar // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 39 назв. — англ.
Підтримка:
The work of N.A. is supported by the grants-in-aid from JSPS (Contract No.26400209). J.S. acknowledges
the hospitality of OPU, where part of this work was completed. R.C. was financially
supported through the MOST grants 102-2811-M-005-025 and 102-2628-M-005-001-MY4 in Taiwan.
He would like to thank Professor Naruhiko Aizawa for the invitation to visit Osaka Prefecture
University and also for the hospitality extended to him during his stay.
Дата:
2015
Переглядів:
305
Завантажень:
211
Анотація:
The conformal Galilei algebra (CGA) is a non-semisimple Lie algebra labelled by two parameters d and ℓ. The aim of the present work is to investigate the lowest weight representations of CGA with d=1 for any integer value of ℓ. First we focus on the reducibility of the Verma modules. We give a formula for the Shapovalov determinant and it follows that the Verma module is irreducible if ℓ=1 and the lowest weight is nonvanishing. We prove that the Verma modules contain many singular vectors, i.e., they are reducible when ℓ≠1. Using the singular vectors, hierarchies of partial differential equations defined on the group manifold are derived. The differential equations are invariant under the kinematical transformation generated by CGA. Finally we construct irreducible lowest weight modules obtained from the reducible Verma modules.
