A basis of a certain module for the hyperalgebra $({\mathrm{SL}}_2{)}_r$ and some applications

Abstract

In the hyperalgebra ${\mathcal{U}}_r$ of the $r$-th Frobenius kernel $({\mathrm{SL}}_2{)}_r$ of the algebraic group ${\mathrm{SL}}_2$, we construct a basis of the ${\mathcal{U}}_r$-module generated by a certain element which was given by the author before. As its applications, we also prove some results on the ${\mathcal{U}}_r$-modules and the algebra ${\mathcal{U}}_r$.

30 pages