Geodesic
Generalized Adjoint Actions
Journal of Lie Theory, Tome 26 (2016) no. 1, pp. 219-225

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The aim of this paper is to generalize the classical formula $$ e^xye^{-x} = \sum_{k\ge 0}{1\over k!}\,({\rm ad}~x)^k (y) $$ by replacing $e^x$ with any formal power series $$ f(x)=1+\sum_{k\ge 1} a_k t^k. $$ We also obtain combinatorial applications to $q$-exponentials, $q$-binomials, and Hall-Littlewood polynomials.
Classification : 20F40, 05E05
Mots-clés : Adjoint action, commutator, q-exponential, Hall-Littlewood polynomial 
A. Berenstein; V. Retakh. Generalized Adjoint Actions. Journal of Lie Theory, Tome 26 (2016) no. 1, pp. 219-225. http://geodesic.mathdoc.fr/item/JOLT_2016_26_1_a10/
@article{JOLT_2016_26_1_a10,
     author = {A. Berenstein and V. Retakh},
     title = {Generalized {Adjoint} {Actions}},
     journal = {Journal of Lie Theory},
     pages = {219--225},
     year = {2016},
     volume = {26},
     number = {1},
     zbl = {1404.17006},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_1_a10/}
}
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