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Method of quantum characters in equivariant quantization | J. Donin
; A. Mudrov
; | Date: |
24 Apr 2002 | Journal: | Commun.Math.Phys. V.234 (2003) 533-555 | Subject: | Quantum Algebra | math.QA | Abstract: | 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. | Source: | arXiv, math.QA/0204298 | Services: | Forum | Review | PDF | Favorites |
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