Abstract
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Let
be a simple complex Lie algebra of finite dimension. This paper
gives an inequality relating the order of an automorphism of
to the
dimension of its fixed-point subalgebra and characterizes those automorphisms of
for which equality
occurs. This amounts to an inequality/equality for Thomae’s function on the automorphism
group of
.
The result has applications to characters of zero-weight spaces, graded Lie algebras,
and inequalities for adjoint Swan conductors.
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Keywords
Lie groups, automorphisms, Thomae
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Mathematical Subject Classification
Primary: 22Exx
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Milestones
Received: 4 August 2021
Revised: 12 September 2022
Accepted: 26 November 2022
Published: 3 May 2023
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| © 2023 The Author(s), under
exclusive license to MSP (Mathematical Sciences Publishers).
Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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