Bethe subalgebras in twisted Yangians

Maxim Nazarov; Grigori Olshanski

doi:10.1007/BF02099459

Bethe subalgebras in twisted Yangians

Maxim Nazarov, Grigori Olshanski

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study analogues of the Yangian of the Lie algebra gl N for the other
classical Lie algebras ~o x and 6pN. We call them twisted Yangians. They are
coideal subalgebras in the Yangian of glN and admit homomorphisms onto the
universal enveloping algebras U(~0N) and U(~PN ) respectively. In every twisted
Yangian we construct a family of maximal commutative subalgebras parametrized
by the regular semisimple elements of the corresponding classical Lie algebra. The
images in U(~ox) and U(~PN ) of these subalgebras are also maximal commutative.

Original language	English
Pages (from-to)	483-506
Number of pages	24
Journal	Communications in Mathematical Physics
Volume	178
Issue number	2
DOIs	https://doi.org/10.1007/BF02099459
Publication status	Published - May 1996

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10.1007/BF02099459

http://arxiv.org/abs/q-alg/9507003

Cite this

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title = "Bethe subalgebras in twisted Yangians",

abstract = "We study analogues of the Yangian of the Lie algebra gl N for the otherclassical Lie algebras ~o x and 6pN. We call them twisted Yangians. They arecoideal subalgebras in the Yangian of glN and admit homomorphisms onto theuniversal enveloping algebras U(~0N) and U(~PN ) respectively. In every twistedYangian we construct a family of maximal commutative subalgebras parametrizedby the regular semisimple elements of the corresponding classical Lie algebra. Theimages in U(~ox) and U(~PN ) of these subalgebras are also maximal commutative.",

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N2 - We study analogues of the Yangian of the Lie algebra gl N for the otherclassical Lie algebras ~o x and 6pN. We call them twisted Yangians. They arecoideal subalgebras in the Yangian of glN and admit homomorphisms onto theuniversal enveloping algebras U(~0N) and U(~PN ) respectively. In every twistedYangian we construct a family of maximal commutative subalgebras parametrizedby the regular semisimple elements of the corresponding classical Lie algebra. Theimages in U(~ox) and U(~PN ) of these subalgebras are also maximal commutative.

AB - We study analogues of the Yangian of the Lie algebra gl N for the otherclassical Lie algebras ~o x and 6pN. We call them twisted Yangians. They arecoideal subalgebras in the Yangian of glN and admit homomorphisms onto theuniversal enveloping algebras U(~0N) and U(~PN ) respectively. In every twistedYangian we construct a family of maximal commutative subalgebras parametrizedby the regular semisimple elements of the corresponding classical Lie algebra. Theimages in U(~ox) and U(~PN ) of these subalgebras are also maximal commutative.

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DO - 10.1007/BF02099459

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