Method of Quantum Characters in Equivariant Quantization
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Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose 𝔸 h (M) is a 𝕌 h (g)-equivariant quantization of the function algebra 𝔸(M) on M. We develop a method of building 𝕌 h (g)-equivariant quantization on G-orbits in M as quotients of 𝔸 h (M). We are concerned with those quantizations that may be simultaneously represented as subalgebras in 𝕌* h (g) and quotients of 𝔸 h (M). It turns out that they are in one-to-one correspondence with characters of the algebra 𝔸 h (M). We specialize our approach to the situation g=gl(n,ℂ), M=End(ℂ n ), and 𝔸 h (M) the so-called reflection equation algebra associated with the representation of 𝕌 h (g) on ℂ n . 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.
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- Method of Quantum Characters in Equivariant Quantization
Communications in Mathematical Physics
Volume 234, Issue 3 , pp 533-555
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