The ${\mathbb{F}}_p$-Selberg integral of type $A_n$

Abstract

We prove an ${\mathbb{F}}_p$-Selberg integral formula of type $A_n$, in which the ${\mathbb{F}}_p$-Selberg integral is an element of the finite field ${\mathbb{F}}_p$ with odd prime number $p$ of elements. The formula is motivated by analogy between multidimensional hypergeometric solutions of the KZ equations and polynomial solutions of the same equations reduced modulo $p$. For the type $A_1$ the formula was proved in a previous paper by the authors.

Latex, 21 pages, v2: misprints corrected, remarks, references added. arXiv admin note: text overlap with arXiv:2011.14248

References in corpus (3)

• Solutions modulo $p$ of Gauss-Manin differential equations for multidimensional hypergeometric integrals and associated Bethe ansatz
• An invariant subbundle of the KZ connection mod $p$ and reducibility of ${\widehat{sl}}_2$ Verma modules mod $p$
• Determinant of ${\mathbb{F}}_p$-hypergeometric solutions under ample reduction

Cited by in corpus (3)

• Notes on solutions of KZ equations modulo $p^s$ and $p$-adic limit $s\to \infty$
• Determinant of ${\mathbb{F}}_p$-hypergeometric solutions under ample reduction
• Congruences for Hasse--Witt matrices and solutions of $p$-adic KZ equations