On the irreducible representations of the alternating group which remain irreducible in characteristic ๐
On the irreducible representations of the alternating group which remain irreducible in characteristic ๐
We consider the problem of which ordinary irreducible representations of the alternating group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper A Subscript n"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">A</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">\mathfrak {A}_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> remain irreducible modulo a prime <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation โฆ