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Journal Article

Generalized adjoint actions

MPS-Authors
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Retakh,  Vladimir
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

http://www.heldermann.de/JLT/JLT26/JLT261/jlt26011.htm
(Publisher version)

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Fulltext (public)

arXiv:1506.07071.pdf
(Preprint), 120KB

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Citation

Berenstein, A., & Retakh, V. (2016). Generalized adjoint actions. Journal of Lie Theory, 26(1), 219-225. Retrieved from http://arxiv.org/abs/1506.07071.


Cite as: https://hdl.handle.net/21.11116/0000-0004-70E1-F
Abstract
The aim of this paper is to generalize the classical formula $e^xye^{-x}=\sum\limits_{k\ge 0} \frac{1}{k!} (ad~x)^k(y)$ by replacing $e^x$ with any formal power series $\displaystyle {f(x)=1+\sum_{k\ge 1} a_kx^k}$. We also obtain combinatorial applications to $q$-exponentials, $q$- binomials, and Hall-Littlewood polynomials.