Constructing invariant differential operators on homogeneous spaces using THE star-product
The problem of constructing invariant differential operators on homogeneous spaces is considered. We develop a constructive algorithm for the solution of this problem based on using the star-product of operator symbols and reduced to the integration of classical Hamiltonian systems on dual spaces of Lie algebras. A non-trivial example is presented.
Download file
Counter downloads: 54
Keywords
star product, Lie group, Lie algebra, invariant differential operatorAuthors
| Name | Organization | |
| Magazev A.A. | Omsk State Technical University | magazev@omgtu.ru |
| Popov A.S. | Omsk F.M. Dostoevsky State University | popovanton800@gmail.com |
| Shirokov I.V. | Omsk State Technical University | iv_shirokov@mail.ru |
References
Попов А.С., Широков И.В. // Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки. - 2013. - № 1 (30). - С. 379-386.
Винберг Э.Б. // УМН. - 2001. - Т. 56. - № 1(337). - С. 3-62.
Barut A.O., Roczka R. Theory of Group Representations and Applications. - Polish Scientific Publishers, 1980. - 717 p.
Milson R. // J. Math. Phys. - 1995. - V. 36. - No. 10. - P. 6004-6027.
Широков И.В. К-орбиты, гармонический анализ на однородных пространствах и интегрирование дифференциальных уравнений. - Омск: Изд-во ОмГу, 1998. - 96 с.
Широков И.В. // ТМФ. - 2001. - Т. 129. - № 1. - С. 3-13.
