发表机构
Iowa State University（爱荷华州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将ABRR递推公式推广至相对极值投影子，得到其紧致显式解，适用于多种李代数与李超代数，在表示理论等领域具应用价值。
AI 中文摘要
2004年，Khoroshkin证明极值投影子等价于动力学扭。动力学扭满足的Arnaudon-Buffenoir-Ragoucy-Roche（ABRR）方程给出了极值投影子系数的递推公式，所得求和公式在表示理论及Mickelsson-Zhelobenko约化代数的应用中兼具一致性与强大性。本文将该递推公式推广至Conley与Sepanski于2003年引入的相对极值投影子。当Levi子代数为Cartan子代数时，可得到常规ABRR递推；还找到了该递推解的紧致显式表达式，研究范围涵盖无限维对偶李超代数、Kac-Moody代数、基础经典李超代数及有限维约化李代数。
英文摘要
In 2004, Khoroshkin proved that the extremal projector is equivalent to the dynamical twist. The Arnaudon-Buffenoir-Ragoucy-Roche (ABRR) equation, satisfied by the dynamical twist, yields a recursive formula for the coefficients in the extremal projector. The resulting summation formula is uniform and powerful in its applications to representation theory and Mickelsson-Zhelobenko reduction algebras. In this paper we generalize this recursive formula to the relative extremal projector, introduced by Conley and Sepanski in 2003. When the Levi subalgebra is the Cartan subalgebra, we recover the usual ABRR recursion. We also find a compact and explicit expression for the solution to the recursion. Our setting includes infinite-dimensional contragredient Lie superalgebras, Kac-Moody algebras, basic classical Lie superalgebras, and finite-dimensional reductive Lie algebras.
Comments19 pages
