Kyungpook Mathematical Journal

  • 제55권2호
  • /
  • Pages.233-249
  • /
  • 2015
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Studying Solutions of a System of PDE Through Representations of D4

  • 투고 : 2013.06.11
  • 심사 : 2013.08.07
  • 발행 : 2015.06.23
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초록

This paper is concerned with applications of representations of the Lie group of class $D_4$ to PDE. A realization of all irreducible finite-dimensional representations of $D_4$ is found and their application to a study of solutions of some systems of partial differential equations is given.

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참고문헌

  1. C. Chevalley and R. D. Schafer, The Exceptional Simple Lie Algebras $F_4\;and\;E_6$, Proc. Natl. Acad. Sci. U. S. A., 36(2)(1950), 137-141. https://doi.org/10.1073/pnas.36.2.137
  2. N. Jacobson, Lie Algebras, Interscience, New York, 1962.
  3. A. Loutsiouk, On extreme vectors of Verma modules over complex semisimple Lie algebras, International Journal of Algebra, 2(16)(2008), 771-778.
  4. D. Zlelobenko, Compact Lie groups and their representations, American Mathematical Society, Providence, R. I., 1973.
  5. D. Zlelobenko, Operators of discrete symmetry for reductive Lie groups, Izvestia AN USSR, ser. malem., 40(5)(1976), 1055-1083.