M. Larsen

activity

19922023

most citedAlternating sign matrices and domino tilings

280 citations · 1k across the 82 of their papers we have counts for

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13 papers · 1 filter

math.RT2022

Level, rank, and tensor growth of representations of symmetric groups

Alexander Kleshchev, Michael Larsen, Pham Huu Tiep

We develop a theory of levels for irreducible representations of symmetric groups of degree $n$ analogous to the theory of levels for finite classical groups. A key property of lev…

math.RT2022

Character bounds for regular semisimple elements and asymptotic results on Thompson's conjecture

Michael Larsen, Jay Taylor, Pham Tiep

For every integer $k$ there exists a bound $B = B (k)$ such that if the characteristic polynomial of $g \in SL_{n} (q)$ is the product of $\leq k$ pairwise distinct monic ir…

math.RT2021

Representations and tensor product growth

Michael Larsen, Aner Shalev, Pham Huu Tiep

The deep theory of approximate subgroups establishes 3-step product growth for subsets of finite simple groups $G$ of Lie type of bounded rank. In this paper we obtain 2-step growt…

math.RT2020

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

Michael J. Larsen, Alexander R. Miller

In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero.

math.RT2019

Many zeros of many characters of GL(n,q)

Patrick X. Gallagher, Michael J. Larsen, Alexander R. Miller

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

math.RT2019

Character Levels and Character Bounds. II

Robert M. Guralnick, Michael Larsen, Pham Huu Tiep

This paper is a continuation of [GLT], which develops a level theory and establishes strong character bounds for finite simple groups of linear and unitary type in the case that th…