Generalized adjoint actions

Arkady Berenstein; Vladimir Retakh

Generalized adjoint actions

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of this paper is to generalize the classical formula e^xye^-x = ∑_k≥01/k!(ad x)^k(y) by replacing e^x with any formal power series f(x) = 1 + ∑k_≥1a_kt^k. We also obtain combinatorial applications to q-exponentials, q-binomials, and Hall-Littlewood polynomials.

Original language	English (US)
Pages (from-to)	219-225
Number of pages	7
Journal	Journal of Lie Theory
Volume	26
Issue number	1
State	Published - 2016

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Adjoint action
Commutator
Hall-Littlewood polynomial
q-exponential

Cite this

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title = "Generalized adjoint actions",

abstract = "The aim of this paper is to generalize the classical formula exye-x = ∑k≥01/k!(ad x)k(y) by replacing ex with any formal power series f(x) = 1 + ∑k≥1aktk. We also obtain combinatorial applications to q-exponentials, q-binomials, and Hall-Littlewood polynomials.",

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author = "Arkady Berenstein and Vladimir Retakh",

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year = "2016",

language = "English (US)",

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journal = "Journal of Lie Theory",

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AU - Berenstein, Arkady

AU - Retakh, Vladimir

PY - 2016

Y1 - 2016

N2 - The aim of this paper is to generalize the classical formula exye-x = ∑k≥01/k!(ad x)k(y) by replacing ex with any formal power series f(x) = 1 + ∑k≥1aktk. We also obtain combinatorial applications to q-exponentials, q-binomials, and Hall-Littlewood polynomials.

AB - The aim of this paper is to generalize the classical formula exye-x = ∑k≥01/k!(ad x)k(y) by replacing ex with any formal power series f(x) = 1 + ∑k≥1aktk. We also obtain combinatorial applications to q-exponentials, q-binomials, and Hall-Littlewood polynomials.

KW - Adjoint action

KW - Commutator

KW - Hall-Littlewood polynomial

KW - q-exponential

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M3 - Article

AN - SCOPUS:84955499734

SN - 0949-5932

VL - 26

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JO - Journal of Lie Theory

JF - Journal of Lie Theory

IS - 1

ER -

Generalized adjoint actions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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