Parabolic Presentations of the Super Yangian $${Y(\mathfrak{gl}_{M|N})}$$ Y ( gl M | N ) Associated with Arbitrary 01-Sequences

Peng, Yung-Ning

doi:10.1007/s00220-015-2548-9

Cited by 16 publications

(13 citation statements)

References 16 publications

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“…Presentations of the Yangian for sl n|m analogous to [7] and [24] were given by Stukopin [29], while the construction of [4] was extended to the Yangian Y(gl n|m ) by Gow [13], where a Drinfeld-type presentation was devised together with an isomorphism with the R-matrix presentation. More general parabolic presentations of the Yangian Y(gl n|m ), corresponding to arbitrary Borel subalgebras in gl n|m were given by Peng [28]; see also Tsymbaliuk [30].…”

Section: Introductionmentioning

confidence: 99%

A Drinfeld-type presentation of the orthosymplectic Yangians

Molev¹

2021

Preprint

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We use the Gauss decomposition of the generator matrix in the R-matrix presentation of the Yangian for the orthosymplectic Lie superalgebra osp N |2m to produce its Drinfeld-type presentation. The results rely on the work of Gow ( 2007) concerning the gl n|m Yangians and our work with Jing and Liu (2018) devoted to the orthogonal and symplectic Yangians. One exception is the embedding theorem whose proof required a different approach in the super case.

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Section: Introductionmentioning

confidence: 99%

A Drinfeld-type presentation of the orthosymplectic Yangians

Molev¹

2021

Preprint

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“…Following [D,BK,G2,P2], define the Drinfeld super Yangian of gl(V ), denoted by Y (gl(V )), to be the associative C-superalgebra generated by {d…”

Section: The Drinfeld Super Yangian Of Gl(v )mentioning

confidence: 99%

“…We define those in the Drinfeld realization, generalizing the construction of [S] for a distinguished Dynkin diagram. Following [BK,G2,P2], we obtain their RTT realization and thus identify all of them with the super Yangian of M. Nazarov [Na]. We also describe their centers, following [G2].…”

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confidence: 99%

Shuffle algebra realizations of type A super Yangians and quantum affine superalgebras for all Cartan data

Tsymbaliuk

2020

Lett Math Phys

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We introduce super Yangians of gl(V ), sl(V ) (in the new Drinfeld realization) associated to all Dynkin diagrams of gl(V ). We show that all of them are isomorphic to the super Yangians introduced by M. Nazarov in [Na], by identifying them with the corresponding RTT super Yangians. However, their "positive halves" are not pairwise isomorphic, and we obtain the shuffle algebra realizations for all of those in spirit of [T]. We adapt the latter to the trigonometric setup by obtaining the shuffle algebra realizations of the "positive halves" of type A quantum loop superalgebras associated to arbitrary Dynkin diagrams.

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“…An earlier note by Stukopin [16] contains an alternative approach to the Yangian presentations (with a correction in the set of defining relations pointed out in [7]). More recently, Drinfeld-type parabolic presentations of the Yangian Y(gl m|n ), corresponding to arbitrary Borel subalgebras in gl m|n were given by Peng [14]. In a particular case, such a presentation was reproduced by Tsymbaliuk [19] who also gave a description of the center of the Yangian by using the quantum Berezinian, thus generalizing the results of [12] and [6].…”

Section: Introductionmentioning

confidence: 96%

Odd reflections in the Yangian associated with ${\frak gl}(m|n)$

Molev

2021

Preprint

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The odd reflections is an effective tool in the Lie superalgebra representation theory, as they relate non-conjugate Borel subalgebras. We introduce analogues of the odd reflections for the Yangian Y(gl m|n ) and use them to produce a transition rule for the parameters of the highest weight modules corresponding to a change of the parity sequence. This leads to a description of the finite-dimensional irreducible representations of the Yangian associated with an arbitrary parity sequence.

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Parabolic Presentations of the Super Yangian $${Y(\mathfrak{gl}_{M|N})}$$ Y ( gl M | N ) Associated with Arbitrary 01-Sequences

Abstract: Abstract. Let µ be an arbitrary composition of M +N and let s be an arbitrary 0 M 1 N -sequence. A new presentation, depending on µ and s, of the super Yangian Y M|N associated to the general linear Lie superalgebra gl M|N is obtained.

Cited by 16 publications

References 16 publications

A Drinfeld-type presentation of the orthosymplectic Yangians

A Drinfeld-type presentation of the orthosymplectic Yangians

Shuffle algebra realizations of type A super Yangians and quantum affine superalgebras for all Cartan data

Odd reflections in the Yangian associated with ${\frak gl}(m|n)$

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