Let $G=GL(2,p)$ be the group of linear transformations. It acts on the set $X=F_p^2$. Then $C^X$ is a linear representation of $G$. What is the decomposition of this representation into irreducible representations?

Note: Let $d_i$ denote the number of isomorphic irreducible representations. Then $\sum d_i^2$ is equal to the number of orbits of $G$ when $G$ acts on $X\otimes X$. The number of orbits of $G$ in $X\otimes X$ is equal to $p+1$.

Let $G=GL(2,p)$ be the group of linear transformations. It acts on the set $X=F_p^2$. Then $C^X$ is a linear representation of $G$. What is the decomposition of this representation into irreducible representations?

Note: Let $d_i$ denote the number of isomorphic irreducible representations. Then $\sum d_i^2$ is equal to the number of orbits of $G$ when $G$ acts on $X\times X$. The number of orbits of $G$ in $X\times X$ is equal to $p+1$.

Let $G=GL(2,p)$ be a group of linear transformations. It acts on the set $X=F_p^2$. Then $C^X$ is a linear represintation of $G$. What is the decomposition of this represintation into irreducible represintations?

Note: Let $d_i$ number of isomorphic irreducible represintations. Then $\sum d_i^2$ equal to the number of orbits of $G$ when it acts on $X\otimes X$. The number of orbits of $G$ in $X\otimes X$ is $p+1$.

Let $G=GL(2,p)$ be the group of linear transformations. It acts on the set $X=F_p^2$. Then $C^X$ is a linear representation of $G$. What is the decomposition of this representation into irreducible representations?

Note: Let $d_i$ denote the number of isomorphic irreducible representations. Then $\sum d_i^2$ is equal to the number of orbits of $G$ when $G$ acts on $X\otimes X$. The number of orbits of $G$ in $X\otimes X$ is equal to $p+1$.