Minimal polynomials of elements of order 𝑝 in 𝑝-modular projective representations of alternating groups

Kleshchev, A.; Zalesski, A.

doi:10.1090/S0002-9939-03-07242-3

Minimal polynomials of elements of order $p$ in $p$-modular projective representations of alternating groups
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by A. S. Kleshchev and A. E. Zalesski PDF

Proc. Amer. Math. Soc. 132 (2004), 1605-1612 Request permission

Abstract:

Let $F$ be an algebraically closed field of characteristic $p>0$ and let $G$ be a quasi-simple group with $G/Z(G)\cong A_n$. We describe the minimal polynomials of elements of order $p$ in irreducible representations of $G$ over $F$. If $p=2$, we determine the minimal polynomials of elements of order $4$ in $2$-modular irreducible representations of $A_{n}$, $S_n$, $3\cdot A_6$, $3\cdot S_6$, $3\cdot A_7$, and $3\cdot S_7$.

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