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YCor
YCor
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$GL $\mathrm{GL}(n, \mathbb{Z})$-Equivariant Mapsequivariant maps on $GL$\mathrm{GL}(n, \mathbb{R})$

Can$\DeclareMathOperator\GL{GL}$Can you describe the maps from $GL(n, \mathbb{R})$$\GL(n, \mathbb{R})$ to $GL(n, \mathbb{R})$$\GL(n, \mathbb{R})$ that are equivariant w.r.t. right multiplication by $GL(n, \mathbb{Z})$$\GL(n, \mathbb{Z})$? I'm interested even in classes of examples, not necessarily a full description.

Of course, there are maps that are equivariant to the whole $GL(n, \mathbb{R})$$\GL(n, \mathbb{R})$. What else is there?

Thank you for your help.

$GL(n, \mathbb{Z})$-Equivariant Maps on $GL(n, \mathbb{R})$

Can you describe the maps from $GL(n, \mathbb{R})$ to $GL(n, \mathbb{R})$ that are equivariant w.r.t. right multiplication by $GL(n, \mathbb{Z})$? I'm interested even in classes of examples, not necessarily a full description.

Of course, there are maps that are equivariant to the whole $GL(n, \mathbb{R})$. What else is there?

Thank you for your help.

$\mathrm{GL}(n, \mathbb{Z})$-equivariant maps on $\mathrm{GL}(n, \mathbb{R})$

$\DeclareMathOperator\GL{GL}$Can you describe the maps from $\GL(n, \mathbb{R})$ to $\GL(n, \mathbb{R})$ that are equivariant w.r.t. right multiplication by $\GL(n, \mathbb{Z})$? I'm interested even in classes of examples, not necessarily a full description.

Of course, there are maps that are equivariant to the whole $\GL(n, \mathbb{R})$. What else is there?

Thank you for your help.

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gm01
gm01
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$GL(n, \mathbb{Z})$-Equivariant Maps on $GL(n, \mathbb{R})$

Can you describe the maps from $GL(n, \mathbb{R})$ to $GL(n, \mathbb{R})$ that are equivariant w.r.t. right multiplication by $GL(n, \mathbb{Z})$? I'm interested even in classes of examples, not necessarily a full description.

Of course, there are maps that are equivariant to the whole $GL(n, \mathbb{R})$. What else is there?

Thank you for your help.