Geodesic
Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem
Serdica Mathematical Journal, Tome 23 (1997) no. 2, pp. 95-112.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.
Keywords: Bispectral Operators, Darboux Transformations, W–Algebras, Highest Weight Representations, KP–Hierarchy 
@article{SMJ2_1997_23_2_a1,
     author = {Bakalov, B. and Horozov, E. and Yakimov, M.},
     title = {Highest {Weight} {Modules} of {W1+\ensuremath{\infty},} {Darboux} {Transformations} and the {Bispectral} {Problem}},
     journal = {Serdica Mathematical Journal},
     pages = {95--112},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_1997_23_2_a1/}
}
TY  - JOUR
AU  - Bakalov, B.
AU  - Horozov, E.
AU  - Yakimov, M.
TI  - Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem
JO  - Serdica Mathematical Journal
PY  - 1997
SP  - 95
EP  - 112
VL  - 23
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_1997_23_2_a1/
LA  - en
ID  - SMJ2_1997_23_2_a1
ER  - 
%0 Journal Article
%A Bakalov, B.
%A Horozov, E.
%A Yakimov, M.
%T Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem
%J Serdica Mathematical Journal
%D 1997
%P 95-112
%V 23
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_1997_23_2_a1/
%G en
%F SMJ2_1997_23_2_a1
Bakalov, B.; Horozov, E.; Yakimov, M. Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem. Serdica Mathematical Journal, Tome 23 (1997) no. 2, pp. 95-112. http://geodesic.mathdoc.fr/item/SMJ2_1997_23_2_a1/