Isomorphism Between the R-Matrix and Drinfeld Presentations of Yangian in Types B, C and D

It is well-known that the Gauss decomposition of the generator matrix in the R -matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation. Defining relations between these generators are known in an explicit form, thus providing an isomorphism between the presentati...

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Bibliographic Details
Published in:Communications in mathematical physics 2018-08, Vol.361 (3), p.827-872
Main Authors: Jing, Naihuan, Liu, Ming, Molev, Alexander
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Generators
Isomorphism
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:It is well-known that the Gauss decomposition of the generator matrix in the R -matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation. Defining relations between these generators are known in an explicit form, thus providing an isomorphism between the presentations. It has been an open problem since the pioneering work of Drinfeld to extend this result to the remaining types. We give a solution for the classical types B , C and D by constructing an explicit isomorphism between the R -matrix and Drinfeld presentations of the Yangian. It is based on an embedding theorem which allows us to consider the Yangian of rank n - 1 as a subalgebra of the Yangian of rank n of the same type.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-018-3185-x