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YCor
YCor
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What are the irreps in this canonical action of $PGL_2$\operatorname{PGL}_2(F_q)$?

Consider the permutation action of $PGL_2(\mathbb F_q)$$\operatorname{PGL}_2(\mathbb F_q)$ on $\mathbb P^1(\mathbb F_q)$ by fractional linear transformations. We can consider the associated (complex) representation of dimension $q+1$.

What can we say about the irreducible representations occurring in this representation? This is probably doable because our representation is an induced representation. What I am really interested in is the following question:

What can we say about the invariant polynomials for this representation?

What are the irreps in this canonical action of $PGL_2(F_q)$?

Consider the permutation action of $PGL_2(\mathbb F_q)$ on $\mathbb P^1(\mathbb F_q)$ by fractional linear transformations. We can consider the associated (complex) representation of dimension $q+1$.

What can we say about the irreducible representations occurring in this representation? This is probably doable because our representation is an induced representation. What I am really interested in is the following question:

What can we say about the invariant polynomials for this representation?

What are the irreps in this canonical action of $\operatorname{PGL}_2(F_q)$?

Consider the permutation action of $\operatorname{PGL}_2(\mathbb F_q)$ on $\mathbb P^1(\mathbb F_q)$ by fractional linear transformations. We can consider the associated (complex) representation of dimension $q+1$.

What can we say about the irreducible representations occurring in this representation? This is probably doable because our representation is an induced representation. What I am really interested in is the following question:

What can we say about the invariant polynomials for this representation?

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Asvin
Asvin
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What are the irreps in this canonical action of $PGL_2(F_q)$?

Consider the permutation action of $PGL_2(\mathbb F_q)$ on $\mathbb P^1(\mathbb F_q)$ by fractional linear transformations. We can consider the associated (complex) representation of dimension $q+1$.

What can we say about the irreducible representations occurring in this representation? This is probably doable because our representation is an induced representation. What I am really interested in is the following question:

What can we say about the invariant polynomials for this representation?