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Vanya
Vanya
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Is the following claim true?:

Let $G$ be an algebraic group such that $G^\circ$ is reductive. Suppose $G$ acts irreducibly on $V$. Is it true that $G^\circ$ acts isotypically, i.e does $V$ decomposeis decomposed (written as direct sum) into $G^\circ$ components of equal dimension?

Is the following claim true?:

Let $G$ be an algebraic group such that $G^\circ$ is reductive. Suppose $G$ acts irreducibly on $V$. Is it true that $G^\circ$ acts isotypically, i.e does $V$ decompose into $G^\circ$ components of equal dimension?

Is the following claim true?:

Let $G$ be an algebraic group such that $G^\circ$ is reductive. Suppose $G$ acts irreducibly on $V$. Is it true that $V$ is decomposed (written as direct sum) into $G^\circ$ components of equal dimension?

deleted 9 characters in body
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Vanya
Vanya
  • 601
  • 3
  • 6

Is the following claim true?:

Let $G$ be an algebraic group such that $G^\circ$ is reductive. Suppose $G$ acts irreducibly on $V$. Is it true that $G^\circ$ acts isotypically, i.e will $G^\circ$ decompose does $V$ decompose into $G^\circ$ components of equal dimension?

Is the following claim true?:

Let $G$ be an algebraic group such that $G^\circ$ is reductive. Suppose $G$ acts irreducibly on $V$. Is it true that $G^\circ$ acts isotypically, i.e will $G^\circ$ decompose $V$ into $G^\circ$ components of equal dimension?

Is the following claim true?:

Let $G$ be an algebraic group such that $G^\circ$ is reductive. Suppose $G$ acts irreducibly on $V$. Is it true that $G^\circ$ acts isotypically, i.e does $V$ decompose into $G^\circ$ components of equal dimension?

Source Link
Vanya
Vanya
  • 601
  • 3
  • 6

Irreducible action of an algebraic group

Is the following claim true?:

Let $G$ be an algebraic group such that $G^\circ$ is reductive. Suppose $G$ acts irreducibly on $V$. Is it true that $G^\circ$ acts isotypically, i.e will $G^\circ$ decompose $V$ into $G^\circ$ components of equal dimension?