Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495456 | Journal of Functional Analysis | 2005 | 21 Pages |
Abstract
This paper studies the Lie symmetries of the equationâx2+ax-1âx+bâtf(x,t)=0.Generically the symmetry group is sl(2,R). In particular, we show the local action of the symmetry group extends to a global representation of SL(2,R) on an appropriate subspace of smooth solutions. In fact, every principal series is realized in this way. Moreover, this subspace is naturally described in terms of sections of an appropriate line bundle on which the given differential operator is intimately related to the Casimir element.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Mark R. Sepanski, Ronald J. Stanke,