Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 14, Tome 215 (1994), pp. 115-129
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D. V. Gluschenkov; A. V. Lyakhovskaya. Regular representation of the quantum Heisenberg double $\{U_q(sl(2)),Fun_q(sl(2))\}$ ($q$ is a root of unity). Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 14, Tome 215 (1994), pp. 115-129. http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a6/
@article{ZNSL_1994_215_a6,
author = {D. V. Gluschenkov and A. V. Lyakhovskaya},
title = {Regular representation of the quantum {Heisenberg} double $\{U_q(sl(2)),Fun_q(sl(2))\}$ ($q$~is a~root of unity)},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {115--129},
year = {1994},
volume = {215},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a6/}
}
TY - JOUR
AU - D. V. Gluschenkov
AU - A. V. Lyakhovskaya
TI - Regular representation of the quantum Heisenberg double $\{U_q(sl(2)),Fun_q(sl(2))\}$ ($q$ is a root of unity)
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1994
SP - 115
EP - 129
VL - 215
UR - http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a6/
LA - en
ID - ZNSL_1994_215_a6
ER -
%0 Journal Article
%A D. V. Gluschenkov
%A A. V. Lyakhovskaya
%T Regular representation of the quantum Heisenberg double $\{U_q(sl(2)),Fun_q(sl(2))\}$ ($q$ is a root of unity)
%J Zapiski Nauchnykh Seminarov POMI
%D 1994
%P 115-129
%V 215
%U http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a6/
%G en
%F ZNSL_1994_215_a6
Pairing between the universal enveloping algebra $U_q(sl(2))$ and the algebra of functions over $SL_q(2)$ is obtained in explicit terms. The regular representation of the quantum double is constructed and investigated. The structure of the root subspaces of the Casimir operator is revealed and described in terms of $SL_q(2)$ elements. Bibliography: 7 titles.
