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• W1978399737 abstract "For each of the classical Lie algebras ( {frak g}(n)={frak o}(2n+1)),( {frak {sp}(2n),{frak o}(2n)} ) of type B, C, D we consider the centralizer of the subalgebra ( {frak o}(2n-2m) ) or ( {frak {sp}}(2n-2m) ), respectively, in the universal enveloping algebra ( text{rm U}({frak g}(n)) ). We show that the nth centralizer algebra can be naturally projected onto the (n-1)th one, so that one can form the projective limit of the centralizer algebras as ( ntoinfty ) with m fixed. The main result of the paper is a precise description of this limit (or stable) centralizer algebra, denoted by ( text{rm A}_m ). We explicitly construct an algebra isomorphism ( text{rm A}_m=text{rm Z}otimes text{rm Y}_m ), where Z is a commutative algebra and ( text{rm Y}_m ) is the so-called twisted Yangian associated to the rank $m$ classical Lie algebra of type B, C, or D. The algebra Z may be viewed as the algebra of 'virtual' Laplace operators; it is isomorphic to the algebra of polynomials with countably many indeterminates. The twisted Yangian ( text{rm Y}_m ) (and hence the algebra ( text{rm A}_m )) can be described in terms of a system of generators with quadratic and linear defining relations that are conveniently presented in R-matrix form involving the so-called reflection equation. This extends the earlier work on the type A case (i.e., ( {frak g}(n)={frak gl}(n) )) by the second author." @default.
• W1978399737 created "2016-06-24" @default.
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• W1978399737 date "2000-09-01" @default.
• W1978399737 modified "2023-10-17" @default.
• W1978399737 title "Centralizer construction for twisted Yangians" @default.
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• W1978399737 doi "https://doi.org/10.1007/pl00001390" @default.
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