The $\mathbb F_p$-Selberg Integral

The $\mathbb F_p$-Selberg integral of type $A_n$

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.

关于二维 $\mathbb F_p$-Selberg 积分的注记

Notes on $2D$ $\mathbb F_p$-Selberg integrals

本研究证明了依赖于多组正整数参数、取值于奇素数阶有限域的二维 $\mathbb F_p$-Selberg 积分公式，其灵感源于KZ方程的多维超几何解与模p约化后多项式解的相似性，丰富了有限域上积分公式的研究成果。

Regularizable cycles associated with a Selberg type integral under some resonance condition

We study the twisted homology group attached to a Selberg type integral under some resonance condition, which naturally appears in the su_2-conformal field theory and the representation of the Iwahori-Hecke algebra. We determine the dimension of the space of the regularizable cycles. The dimension-formula is given in terms of the generalized hypergeometric series.

Selberg integral and multiple zeta values

In this paper, we show that the coefficient of the Taylor expansion of Selberg integrals with respect to exponent variables are expressed as a linear combination of multiple zeta values. We use beta-nbc base so that the Selberg integral is holomorphic with respect to the exponent variables.

Dimensional interpolation and the Selberg integral

We show that a version of dimensional interpolation for the Riemann--Roch--Hirzebruch formalism in the case of a grassmannian leads to an expression for the Euler characteristic of line bundles in terms of a Selberg integral. We propose a way to interpolate higher Bessel equations, their wedge powers, and monodromies thereof to non--integer orders, and link the result with the dimensional interpolation of the RRH formalism in the spirit of the gamma conjectures.

A Selberg Integral Type Formula for an sl_2 One-Dimensional Space of Conformal Blocks

For distinct complex numbers $z_1,...,z_{2N}$, we give a polynomial $P(y_1,...,y_{2N})$ in the variables $y_1,...,y_{2N}$, which is homogeneous of degree $N$, linear with respect to each variable, $sl_2$-invariant with respect to a natural $sl_2$-action, and is of order $N-1$ at $(y_1,...,y_{2N})=(z_1,...,z_{2N})$. We give also a Selberg integral type formula for the associated one-dimensional space of conformal blocks.