On the number of p-hypergeometric solutions of KZ equations

It is known that solutions of the KZ equations can be written in form multidimensional hypergeometric integrals. In 2017 a joint paper author with V. Schechtman, construction was modified, and modulo prime number p were constructed. These p, called p-hypergeometric solutions, are polynomials integer coefficients. A general problem to determine independent understand meaning number. this paper, we consider associated space singular vectors weight $$n-2r$$ tensor power $$W^{\otimes n}$$ vector representation $$\mathfrak {sl}_2$$ . case given by r-dimensional We module corresponding its rank, show rank equal dimension suitable square integrable differential r-forms.