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

Banach Center Publications (1997)

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

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topDobrev, 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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