dorsal/arxiv
View SchemaQuantization of function algebras on semisimple orbits in $\g^*$
| Authors | Joseph Donin, Dmitry Gurevich, Steven Shnider |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9607008 |
| URL | https://arxiv.org/abs/q-alg/9607008 |
Abstract
In this paper we describe a multiparameter deformation of the function algebra of a semisimple coadjoint orbit. In the first section we use the representation of the Lie algebra on a generalized Verma module to quantize the Kirillov bracket on the family of semisimple coadjoint orbits of a given orbit type. In the second section we extend this construction to define a deformation in the category of representations of the quantized enveloping algebra. In an earlier paper we used cohomological methods to prove the existence of a two parameter family quantizing a compatible pair of Poisson brackets on any symmetric coadjoint orbit. This paper gives a more explicit algebraic construction which includes more general orbit types and which we prove to be flat in all parameters.
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"abstract": "In this paper we describe a multiparameter deformation of the function\nalgebra of a semisimple coadjoint orbit. In the first section we use the\nrepresentation of the Lie algebra on a generalized Verma module to quantize the\nKirillov bracket on the family of semisimple coadjoint orbits of a given orbit\ntype. In the second section we extend this construction to define a deformation\nin the category of representations of the quantized enveloping algebra. In an\nearlier paper we used cohomological methods to prove the existence of a two\nparameter family quantizing a compatible pair of Poisson brackets on any\nsymmetric coadjoint orbit. This paper gives a more explicit algebraic\nconstruction which includes more general orbit types and which we prove to be\nflat in all parameters.",
"arxiv_id": "q-alg/9607008",
"authors": [
"Joseph Donin",
"Dmitry Gurevich",
"Steven Shnider"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Quantization of function algebras on semisimple orbits in $\\g^*$",
"url": "https://arxiv.org/abs/q-alg/9607008"
},
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