Hidden sl 2 - algebra of finite - difference equations

Recently it was found [1] that polynomial solutions of differential equations are connected to finite-dimensional representations of the algebra sl2 of firstorder differential operators. In this Talk it will be shown that there also exists a connection between polynomial solutions of finite-difference equations (like Hahn, Charlier and Meixner polynomials) and unusual finitedimensional representations of the algebra sl2 of finite-difference operators. So, sl2-algebra is the hidden algebra of finite-difference equations with polynomial solutions.