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Title

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

Authors 1

Affiliations

  1. Bulgarian Academy of Sciences, Institute of Nuclear Research and Nuclear Energy, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria

Abstract

We give a systematic discussion of the relation between q-difference equations which are conditionally Uq()-invariant and subsingular vectors of Verma modules over Uq() (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.

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Banach Center Publications
1997/40/1
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Pages:
203-222
Main language of publication
English
Published
1997
Exact and natural sciences