Representations of quantum groups and (conditionally) invariant q-difference equations

Dobrev, Vladimir

Banach Center Publications, Tome 38 (1997), p. 203-222 / Harvested from The Polish Digital Mathematics Library

Résumé

We give a systematic discussion of the relation between q-difference equations which are conditionally $U_{q} ()$ -invariant and subsingular vectors of Verma modules over $U_{q} ()$ (the Drinfeld-Jimbo q-deformation of a semisimple Lie algebra over ℂg or ℝ). We treat in detail the cases of the conformal algebra, = su(2,2), and its complexification, = sl(4). The conditionally invariant equations are the q-deformed d’Alembert equation and a new equation arising from a subsingular vector proposed by Bernstein-Gel’fand-Gel’fand.

Publié le : 1997-01-01

Zbl 0965.17010

EUDML-ID : urn:eudml:doc:252189

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     author = {Dobrev, Vladimir},
     title = {Representations of quantum groups and (conditionally) invariant q-difference equations},
     journal = {Banach Center Publications},
     volume = {38},
     year = {1997},
     pages = {203-222},
     zbl = {0965.17010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p203bwm}
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Dobrev, Vladimir. Representations of quantum groups and (conditionally) invariant q-difference equations. Banach Center Publications, Tome 38 (1997) pp. 203-222. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p203bwm/

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