The sparsity of character tables of high rank groups of Lie type

@article{Larsen2020TheSO,
  title={The sparsity of character tables of high rank groups of Lie type},
  author={Michael Larsen and Alexander R. Miller},
  journal={Representation Theory of the American Mathematical Society},
  year={2020}
}
In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero. 

On even entries in the character table of the symmetric group

We show that almost every entry in the character table of $S_n$ is even as $n\to\infty$. This resolves a conjecture of Miller. We similarly prove that almost every entry in the character table of

Divisibility of character values of the symmetric group by prime powers

. Let k be a positive integer. We show that, as n goes to infinity, almost every entry of the character table of S n is divisible by k . This proves a conjecture of Miller.

Almost all entries in the character table of the symmetric group are multiples of any given prime

Abstract We show that almost every entry in the character table of S N {S_{N}} is divisible by any fixed prime as N → ∞ {N\to\infty} . This proves a conjecture of Miller.

Nonsolvable Groups have a Large Proportion of Vanishing Elements

Zeros and roots of unity in character tables

. For any finite group G , Thompson proved that, for each χ ∈ Irr( G ), χ ( g ) is a root of unity or zero for more than a third of the elements g ∈ G , and Gallagher proved that, for each larger than

References

SHOWING 1-10 OF 19 REFERENCES

Characters of reductive groups over a finite field

This book presents a classification of all (complex) irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection

Many Zeros of Many Characters of GL(n,q)

For $G=\textrm{GL}(n,q)$, the proportion $P_{n,q}$ of pairs $(\chi ,g)$ in $\textrm{Irr}(G)\times G$ with $\chi (g)\neq 0$ satisfies $P_{n,q}\to 0$ as $n\to \infty $.

Unipotent class representatives for finite classical groups

Abstract We describe explicitly representatives of the conjugacy classes of unipotent elements of the finite classical groups.

Degrees, class sizes and divisors of character values

Abstract. In the character table of a finite group there is a tendency either for the character degree to divide the conjugacy class size or the character value to vanish. There is also a partial

On the representations of reductive groups with disconnected cen-tre

© Société mathématique de France, 1988, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les