Shifted twisted Yangians and Slodowy slices in classical Lie algebras

Lewis Topley; Lukas Tappeiner

doi:10.1017/fms.2026.10247

Shifted twisted Yangians and Slodowy slices in classical Lie algebras

Department of Mathematical Sciences

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

28 Downloads (Pure)

Abstract

In this paper we introduce the shifted twisted Yangian of type AI, following the work of Lu–Wang–Zhang, and we study their semiclassical limits, a class of Poisson algebras. We demonstrate that they coincide with the Dirac reductions of the semiclassical shifted Yangian for 𝔤𝔩𝑛. We deduce that these shifted twisted Yangians admit truncations which are isomorphic to Slodowy slices for many nonrectangular nilpotent elements in types B, C, D. As a direct consequence we obtain parabolic presentations of the semiclassical shifted twisted Yangian, analogous to those introduced by Brundan–Kleshchev for the Yangian of type A. Finally we give Poisson presentations of Slodowy slices for all even nilpotent elements in types B, C, D, generalising the recent work of the second author.

Original language	English
Article number	e103
Number of pages	34
Journal	Forum of Mathematics, Sigma
Volume	14
Early online date	13 Jul 2026
DOIs	https://doi.org/10.1017/fms.2026.10247
Publication status	Published - 13 Jul 2026

Acknowledgements

Both authors would like to thank Jon Brown, Jon Brundan, Kang Lu, Hiraku Nakajima, Yung-Ning Peng, Thomas Tappeiner, Weiqiang Wang and Matt Westaway for useful conversations during the development of this work

Funding

Both authors would like to thank Jon Brown, Jon Brundan, Kang Lu, Hiraku Nakajima, Yung-Ning Peng, Thomas Tappeiner, Weiqiang Wang and Matt Westaway for useful conversations during the development of this work. The first author is grateful to the University of Bath for funding his PhD studies. The second author would like to acknowledge funding from the UKRI Future Leaders Fellowship, grant numbers MR/S032657/1, MR/S032657/2, MR/S032657/3.

Funders	Funder number
University of Bath
UK Research and Innovation	MR/S032657/3, MR/S032657/1, MR/S032657/2

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

Access to Document

10.1017/fms.2026.10247Licence: CC BY

Cite this

@article{871c8b2a1f664df2a412f147d91ad10b,

title = "Shifted twisted Yangians and Slodowy slices in classical Lie algebras",

abstract = "In this paper we introduce the shifted twisted Yangian of type AI, following the work of Lu–Wang–Zhang, and we study their semiclassical limits, a class of Poisson algebras. We demonstrate that they coincide with the Dirac reductions of the semiclassical shifted Yangian for 𝔤𝔩𝑛. We deduce that these shifted twisted Yangians admit truncations which are isomorphic to Slodowy slices for many nonrectangular nilpotent elements in types B, C, D. As a direct consequence we obtain parabolic presentations of the semiclassical shifted twisted Yangian, analogous to those introduced by Brundan–Kleshchev for the Yangian of type A. Finally we give Poisson presentations of Slodowy slices for all even nilpotent elements in types B, C, D, generalising the recent work of the second author.",

author = "Lewis Topley and Lukas Tappeiner",

year = "2026",

month = jul,

day = "13",

doi = "10.1017/fms.2026.10247",

language = "English",

volume = "14",

journal = "Forum of Mathematics, Sigma",

issn = "2050-5094",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Shifted twisted Yangians and Slodowy slices in classical Lie algebras

AU - Topley, Lewis

AU - Tappeiner, Lukas

PY - 2026/7/13

Y1 - 2026/7/13

N2 - In this paper we introduce the shifted twisted Yangian of type AI, following the work of Lu–Wang–Zhang, and we study their semiclassical limits, a class of Poisson algebras. We demonstrate that they coincide with the Dirac reductions of the semiclassical shifted Yangian for 𝔤𝔩𝑛. We deduce that these shifted twisted Yangians admit truncations which are isomorphic to Slodowy slices for many nonrectangular nilpotent elements in types B, C, D. As a direct consequence we obtain parabolic presentations of the semiclassical shifted twisted Yangian, analogous to those introduced by Brundan–Kleshchev for the Yangian of type A. Finally we give Poisson presentations of Slodowy slices for all even nilpotent elements in types B, C, D, generalising the recent work of the second author.

AB - In this paper we introduce the shifted twisted Yangian of type AI, following the work of Lu–Wang–Zhang, and we study their semiclassical limits, a class of Poisson algebras. We demonstrate that they coincide with the Dirac reductions of the semiclassical shifted Yangian for 𝔤𝔩𝑛. We deduce that these shifted twisted Yangians admit truncations which are isomorphic to Slodowy slices for many nonrectangular nilpotent elements in types B, C, D. As a direct consequence we obtain parabolic presentations of the semiclassical shifted twisted Yangian, analogous to those introduced by Brundan–Kleshchev for the Yangian of type A. Finally we give Poisson presentations of Slodowy slices for all even nilpotent elements in types B, C, D, generalising the recent work of the second author.

UR - https://www.scopus.com/pages/publications/105045338325

U2 - 10.1017/fms.2026.10247

DO - 10.1017/fms.2026.10247

M3 - Article

SN - 2050-5094

VL - 14

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e103

ER -

Shifted twisted Yangians and Slodowy slices in classical Lie algebras

Abstract

Acknowledgements

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this