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Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials

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journal contribution
posted on 06.07.2021, 12:42 by Alexey BolsinovAlexey Bolsinov, Anton Izosimov, Ivan Kozlov
For an arbitrary representation ρ of a complex finite-dimensional Lie algebra, we construct a collection of numbers that we call the Jordan-Kronecker invariants of ρ. Among other interesting properties, these numbers provide lower bounds for degrees of polynomial invariants of ρ. Furthermore, we prove that these lower bounds are exact if and only if the invariants are independent outside of a set of large codimension. Finally, we show that under certain additional assumptions our bounds are exact if and only if the algebra of invariants is freely generated.

Funding

Russian Science Foundation, project No.17-11-01303

NSF grant DMS-2008021

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Transformation Groups

Publisher

Springer Verlag

Version

VoR (Version of Record)

Rights holder

© The authors

Publisher statement

This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

Acceptance date

17/12/2020

Publication date

2021-06-17

ISSN

1083-4362

eISSN

1531-586X

Language

en

Depositor

Dr Alexey Bolsinov. Deposit date: 10 January 2021

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