Generalized adjoint actions

zbMATH Open1404.17006arXiv1506.07071MaRDI QIDQ2810928

Arkady Berenstein, Vladimir S. Retakh

Publication date: 6 June 2016

Abstract: The aim of this paper is to generalize the classical formula $e^{x}y{e}^{-x}=sumlimit{s}_{kge0}frac1k!(adx{)}^k(y)$ by replacing $e^x$ with any formal power series $displaystylef(x)=1+su{m}_{kge1}{a}_k{x}^k$. We also obtain combinatorial applications to $q$-exponentials, $q$-binomials, and Hall-Littlewood polynomials.

Full work available at URL: https://arxiv.org/abs/1506.07071

zbMATH Keywords

adjoint actioncommutatorHall-Littlewood polynomial\(q\)-exponential

Mathematics Subject Classification ID

Umbral calculus (05A40) Symmetric functions and generalizations (05E05) Identities, free Lie (super)algebras (17B01)

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