Representations of affine Lie algebras and soliton equations
1985 ◽
Vol 315
(1533)
◽
pp. 391-391
Keyword(s):
A few years ago the 'hidden symmetries’ of the soliton equations had been identified as affine Lie groups, also known as loop groups. The first extensive use of the representation theory of affine Lie algebras for the soliton equations have been developed in a series of works by mathematicians of the Kyoto school. We will review some of their results and develop them further on the basis of the representation theory. Thus an orbit of the simplest affine Lie group SL(2, C)^ in the fundamental representation V will provide the solutions of the Korteweg-de Vries equation, and similarly the solutions of the sine-Gordon equation will come from an orbit of the group (SL(2, C) x SL(2, C)) ^ in V x V*.
2004 ◽
Vol 7
(4)
◽
pp. 457-469
◽
1988 ◽
Vol 16
(2)
◽
pp. 125-132
◽
1995 ◽
Vol 06
(05)
◽
pp. 743-746
Keyword(s):
2012 ◽
Vol 183
(11)
◽
pp. 2480-2493
◽
Keyword(s):
2003 ◽
Vol 2003
(15)
◽
pp. 971-980
◽
1989 ◽
Vol 65
(6)
◽
pp. 187-190
1992 ◽
Vol 32
(3)
◽
pp. 557-581
1981 ◽
Vol 376
(1766)
◽
pp. 401-433
◽