Abstract
We present an explicit U h (gl(n, C))-equivariant quantization on coadjoint orbits of GL(n, C). It forms a two-parameter family quantizing the Poisson pair of the reflection equation and Kirillov–Kostant–Souriau brackets.
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Astashkevich, A.: On Karabegov's quantizations of semisimple coadjoint orbits, Adv. Geom. 172 (1999), 1-18.
Bayen, F., Flato, M., Fronsdal, C. Lichnerowicz, A. and Sternheimer, D.: Deformation theory and quantization, Ann. Phys. 111 (1978), 61-110.
Dolan, B. P. and Jahn, O.: Fuzzy complex Grassmannian spaces and their star products, hep-th/0111020.
Donin, J.: Double quantization on coadjoint representations of simple Lie groups and its orbits, math.QA/9909160.
Donin, J.: U h(g)-invariant quantization of coadjoint orbits and vector bundles over them, J. Geom. Phys. 38(1) (2001), 54-80.
Donin, J.: Double quantization on the coadjoint representation of sl(n), Czech J. Phys. 47(11) (1997), 1115-1122.
Drinfeld, V. G.: Quantum groups, In: A. V. Gleason (ed.), Proc. Internat. Congr. Mathematicians, Berkeley, 1986, Amer. Math. Soc., Providence, 1987, pp. 798-820.
Donin, J., and Mudrov, A.: U q (sl(n))-invariant quantization of symmetric coadjoint orbits via reflection equation algebra, Contemp. Math., in press, math.QA/0108112.
Donin, J., and Mudrov, A.: Method of quantum characters in equivariant quantization, Comm. Math. Phys., in press, math.QA/0204298.
Donin, J., Gurevich, D. and Khoroshkin, S.: Double quantization of ℂP n type by generalized Verma modules, J. Geom. Phys. 28 (1998), 384-406.
Donin, J., Gurevich, D. and Shnider, S.: Quantization of function algebras on semisimple orbits in g*, q-alg/9607008.
Faddeev, L., Reshetikhin, N. and Takhtajan, L.: Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1 (1990), 193-226.
Fioresi, R. and Lledó , M. A.: On the deformation quantization of coadjoint orbits of semisimple groups, Pacific J. Math. 198 (2) (2001), 411-436.
Isaev, A., Ogievetsky, O. and Pyatov, P.: On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities, J. Phys. A 32 (1999), L115-L121.
Isaev, A. and Pyatov, P.: Covariant differential complexes on quantum linear groups, J. Phys. A 28 (1995), 2227-2246.
Karabegov, A.: Pseudo-Kähler quantization on flag manifolds, Comm. Math. Phys. 200(2) (1999), 355-379.
Kulish, P. P. and Sasaki, R.: Covariance properties of reflection equation algebras, Progr. Theor. Phys. 89(3) (1993), 741-761.
Kulish, P. P. and Sklyanin, E. K.: Algebraic structure related to the reflection equation, J. Phys. A 25 (1992), 5963-2389.
Lledó , M. A.: Deformation quantization of nonregular orbits of compact Lie groups, Lett. Math. Phys. 58 (1) (2001), 57-67.
Pyatov, P. N. and Saponov, P. A.: Characteristic relations for quantum matrices, J. Phys. A 28 (1995), 4415-4421.
Pawelczyk, J. and Steinacker, H.: A quantum algebraic description of D-branes on group manifolds, hep-th/0203110.
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Donin, J., Donin, J. & Mudrov, A. Explicit Equivariant Quantization on Coadjoint Orbits of GL(n, C). Letters in Mathematical Physics 62, 17–32 (2002). https://doi.org/10.1023/A:1021677725539
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DOI: https://doi.org/10.1023/A:1021677725539