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YCor
YCor
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projective representation Projective representations of SL_n$\mathrm{SL}_n(K)$

Let$\DeclareMathOperator\SL{SL}\DeclareMathOperator\GL{GL}$Let $K$ be a field of characteristic zero, and let $\overline{K}$ be an algebraic closure of $K$. Is it true that the irreducible, projective, rational representations $$ SL_n(K) \rightarrow GL_m(\overline{K}) $$$$ \SL_n(K) \rightarrow \GL_m(\overline{K}) $$ are just restriction to $SL_n(K)$$\SL_n(K)$ of the Weyl modules plus field automorphisms? References and comments are most appreciative. Thanks!

Note: Rational representation == given by rational map of algebraic varieties.

projective representation of SL_n(K)

Let $K$ be a field of characteristic zero, and let $\overline{K}$ be an algebraic closure of $K$. Is it true that the irreducible, projective, rational representations $$ SL_n(K) \rightarrow GL_m(\overline{K}) $$ are just restriction to $SL_n(K)$ of the Weyl modules plus field automorphisms? References and comments are most appreciative. Thanks!

Note: Rational representation == given by rational map of algebraic varieties.

Projective representations of $\mathrm{SL}_n(K)$

$\DeclareMathOperator\SL{SL}\DeclareMathOperator\GL{GL}$Let $K$ be a field of characteristic zero, and let $\overline{K}$ be an algebraic closure of $K$. Is it true that the irreducible, projective, rational representations $$ \SL_n(K) \rightarrow \GL_m(\overline{K}) $$ are just restriction to $\SL_n(K)$ of the Weyl modules plus field automorphisms? References and comments are most appreciative. Thanks!

Note: Rational representation == given by rational map of algebraic varieties.

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W Sao
W Sao
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projective representation of SL_n(K)

Let $K$ be a field of characteristic zero, and let $\overline{K}$ be an algebraic closure of $K$. Is it true that the irreducible, projective, rational representations $$ SL_n(K) \rightarrow GL_m(\overline{K}) $$ are just restriction to $SL_n(K)$ of the Weyl modules plus field automorphisms? References and comments are most appreciative. Thanks!

Note: Rational representation == given by rational map of algebraic varieties.