Generalized adjoint actions

2015/06/23 by Berenstein, Arkady, Retakh, Vladimir
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1506.07071

Abstract

The aim of this paper is to generalize the classical formula e^xye^-x=∑_{k≥ 0} (1)/(k!) (ad~x)^k(y) by replacing e^x with any formal power series f(x)=1+∑_{k≥ 1} a_kx^k. We also obtain combinatorial applications to q-exponentials, q-binomials, and Hall-Littlewood polynomials.

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