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

Vladimir Dobrev

Banach Center Publications (1997)

  • Volume: 40, Issue: 1, page 203-222
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Dobrev, Vladimir. "Representations of quantum groups and (conditionally) invariant q-difference equations." Banach Center Publications 40.1 (1997): 203-222. <http://eudml.org/doc/252189>.

@article{Dobrev1997,
abstract = {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.},
author = {Dobrev, Vladimir},
journal = {Banach Center Publications},
keywords = {-difference equations; subsingular vectors; Verma modules; Drinfeld-Jimbo -deformation; conformal algebra; -deformed d’Alembert equation},
language = {eng},
number = {1},
pages = {203-222},
title = {Representations of quantum groups and (conditionally) invariant q-difference equations},
url = {http://eudml.org/doc/252189},
volume = {40},
year = {1997},
}

TY - JOUR
AU - Dobrev, Vladimir
TI - Representations of quantum groups and (conditionally) invariant q-difference equations
JO - Banach Center Publications
PY - 1997
VL - 40
IS - 1
SP - 203
EP - 222
AB - 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.
LA - eng
KW - -difference equations; subsingular vectors; Verma modules; Drinfeld-Jimbo -deformation; conformal algebra; -deformed d’Alembert equation
UR - http://eudml.org/doc/252189
ER -

References

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  1. [1] A.O. Barut and R. Rączka, Theory of Group Representations and Applications, II edition, (Polish Sci. Publ., Warsaw, 1980). Zbl0471.22021
  2. [2] I.N. Bernstein, I.M. Gel'fand and S.I. Gel'fand, Funkts. Anal. Prilozh. 5 (1) (1971) 1; English translation: Funct. Anal. Appl. 5 (1971) 1. 
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  15. [15] V.G. Drinfeld, Soviet. Math. Dokl. 32 (1985) 2548; in: Proceedings of the International Congress of Mathematicians, Berkeley (1986), Vol. 1 (The American Mathematical Society, Providence, 1987) p. 798. 
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