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Sean Lawton
Sean Lawton
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Any representation is a sub representationsubrepresentation of a direct sum of the regular representation

I need a reference for the following statement:

Let G$G$ be a linear algebraic group over algebraically closed field k.$k.$ Let V$V$ be a finite dimensional G$G$-module. The VThen $V$ is sub representationsubrepresentation of k[G]^n$k[G]^n$ for some n$n$ where k[G]$k[G]$ is coordinate ring of G.$G.$

I could tracefind this statement in Steinberg's lecture notes on "Conjugacy Classes in Algebraic groups" but am not happy with the proof there.

Thanks in advance.

Any representation is a sub representation of direct sum of regular representation

I need a reference for the following statement:

Let G be a linear algebraic group over algebraically closed field k. Let V be a finite dimensional G-module. The V is sub representation of k[G]^n for some n where k[G] is coordinate ring of G.

I could trace this statement in Steinberg's lecture notes on "Conjugacy Classes in Algebraic groups" but am not happy with the proof there.

Thanks in advance.

Any representation is a subrepresentation of a direct sum of the regular representation

I need a reference for the following statement:

Let $G$ be a linear algebraic group over algebraically closed field $k.$ Let $V$ be a finite dimensional $G$-module. Then $V$ is subrepresentation of $k[G]^n$ for some $n$ where $k[G]$ is coordinate ring of $G.$

I could find this statement in Steinberg's lecture notes on "Conjugacy Classes in Algebraic groups" but am not happy with the proof there.

Thanks in advance.

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Anupam Singh
Anupam Singh
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Any representation is a sub representation of direct sum of regular representation

I need a reference for the following statement:

Let G be a linear algebraic group over algebraically closed field k. Let V be a finite dimensional G-module. The V is sub representation of k[G]^n for some n where k[G] is coordinate ring of G.

I could trace this statement in Steinberg's lecture notes on "Conjugacy Classes in Algebraic groups" but am not happy with the proof there.

Thanks in advance.