In recent work on superconformal quantum field theories, Razamat arrived at elliptic kernel identities of a new and striking character: they relate solely to the root systems A 2 and A 3 and have no coupling type parameters, Razamat S S (2019 Lett. Math. Phys. 109 1377–95). The pertinent two- and three-variable Hamiltonians are analytic difference operators and the kernel functions are built from the elliptic gamma function. Razamat presented compelling evidence for the validity of these identities, and checked them to a certain order in a power series expansion. This paper is mainly concerned with analytical proofs of these identities. More specifically, we furnish a complete proof of the identities for the A 2 elliptic case and for the A 3 hyperbolic case, and consider several specializations. We also discuss the implications the kernel identities might have for a Hilbert space scenario involv...

中文翻译：

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关于Razamat的A 2和A 3内核身份

在最近关于超共形量子场理论的工作中，拉扎马特得出了一个具有新奇特征的椭圆核身份：它们仅与根系A 2和A 3有关，没有耦合类型参数，拉扎马特SS（2019 Lett.Math.Phys。 109 1377–95）。相关的二变量和三变量哈密顿量是解析差分算子，并且内核函数是从椭圆伽马函数构建的。Razamat提供了令人信服的证据来证明这些身份的有效性，并在幂级数扩展中将它们按一定顺序检查。本文主要涉及这些身份的分析证明。更具体地说，我们为A 2椭圆型和A 3双曲型提供了身份的完整证明，并考虑了几种专门化。