Highest weight modules of W_{1+infty}, Darboux transformations and the bispectral problem
arXiv:q-alg/9601017
Abstract
We announce a systematic way for constructing bispectral algebras of commuting differential operators of any rank N. It enables us to obtain all previously known classes and examples of bispectral operators. Moreover, we give a representation-theoretic explanation of the results including those of Duistermaat and Grünbaum. The manifold of bispectral operators of any order is preserved by an hierarchy of symmetries. We point out that our methods provide a completely algorithmic procedure for obtaining bispectral algebras. We conjecture that the class built in the present paper exhausts all bispectral scalar operators. The proofs and details appeared in our preprints hep-th/9510211, q-alg/9602010, q-alg/9602011, q-alg/9602012.
16 pages, LaTeX2e, uses amsfonts.sty, no figures; eq. (19) was corrected, references were added. Presented at the Conference Geom. and Math. Phys., Zlatograd, August 1995
References in corpus (2)
Cited by in corpus (5)
- Bispectral algebras of commuting ordinary differential operators
- Bispectral Darboux Transformations: The Generalized Airy Case
- Tau-functions as highest weight vectors for W_{1+infty} algebra
- Calogero-Moser pairs and the Airy and Bessel bispectral involutions
- Bispectral Operators, Dual Isomonodromic Deformations and the Riemann-Hilbert Dressing Method