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

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

Let F be an algebraically closed field of characteristic p > 0 and G be a quasi-simple group with G/Z(G) ∼= An. 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 2modular irreducible representations of An, Sn, 3 ·A6, 3 ·S6, 3 ·A7, and 3 ·S7.

MINI-COURSE: p-MODULAR REPRESENTATIONS OF p-ADIC GROUPS

1.1. The case ` 6= p. In this case, we are in the setting of the classical Local Langlands Correspondence, which can be stated (roughly) as follows: Let n ≥ 1. We then have an injective map (1)  continuous representations of Gal(Qp/Qp) on n-dimensional Q`-vector spaces, up to isomorphism  ↪−→  irreducible, admissible representations of GLn(Qp) on Q`-vector spaces, up to isomor...

maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$

let $g$ be a non-abelian group of order $p^n$‎, ‎where $nleq 5$ in which $g$ is not extra special of order $p^5$‎. ‎in this paper we determine the maximal size of subsets $x$ of $g$‎ ‎with the property that $xyneq yx$ for any $x,y$ in $x$ with‎ ‎$xneq y$‎.

maximal subsets of pairwise non-commuting elements of p-groups of order less than p^6

let $g$ be a non-abelian group of order $p^n$‎, ‎where $nleq 5$ in which $g$ is not extra special of order $p^5$‎. ‎in this paper we determine the maximal size of subsets $x$ of $g$‎ ‎with the property that $xyneq yx$ for any $x,y$ in $x$ with‎ ‎$xneq y$‎.

Resolutions of p-Modular TQFT’s and Representations of Symmetric Groups