Method of quantum characters in equivariant quantization

J. Donin, A. Mudrov

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13 Scopus citations

Abstract

Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose Ah(M) is a Uh (g)-equivariant quantization of the function algebra A(M) on M. We develop a method of building Uh (g)-equivariant quantization on G-orbits in M as quotients of Ah(M). We are concerned with those quantizations that may be simultaneously represented as subalgebras in U*h(g) and quotients of Ah(M). It turns out that they are in one-to-one correspondence with characters of the algebra Ah(M). We specialize our approach to the situation g = gl (n, ℂ), M = End(ℂn), and Ah(M) the so-called reflection equation algebra associated with the representation of ℂh,(g) on ℂn. For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the U(g)-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits.

Original languageEnglish
Pages (from-to)533-555
Number of pages23
JournalCommunications in Mathematical Physics
Volume234
Issue number3
StatePublished - Mar 2003

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