For any group of \( n \times n\) matrices, one can consider the invariants in the polynomial ring \(\mathbb{C}[x_1,\dots, x_n]\) under the action of the group on the generators \( x_1,\dots, x_n \). The coinvariants are defined as the quotient of the polynomial ring by the ideal generated by the invariants with no constant term. This module is classical and well-understood for some general cases. One of the natural questions is as follows: how are the irreducible representations of the group distributed in this graded module? We will introduce this construction for the symmetric groups and discuss some of its nice properties. We will then consider a generalization given by a diagonal action on many sets of variables, \(X_n, Y_n, \Gamma_n, T_n, \dots.\) Some of these variables may commute, but others may be anti-commuting variables (sometimes called "bosonic'' and "fermionic''). Even in the simplest case when we have two sets of commuting variables, it is still an open question to describe how the irreducible representations are distributed in this bigraded module. We will see that this question is closely related to operators related to Macdonald polynomials and discuss some recent results regarding this connection. Some of this talk is based on joint work with Brendon Rhoades and Alessandro Iraci.