T. Pham

activity

20102026

most citedConjugacy action, induced representations and the Steinberg square for simple groups of Lie type

39 citations · 130 across the 39 of their papers we have counts for

collaborators

46 papers

math.GR2026

Degrees of $p$ -rational characters and normality of Sylow $p$ -subgroups

Silvio Dolfi, Pham Huu Tiep, Yu Zeng

Several refinements of (the normality part of) the celebrated Itô--Michler theorem were obtained during the last two decades, in which the condition of having $p^{'}$ -degree, for a fi…

math.RT2026

Zeros of characters and orders of elements in finite groups

Gunter Malle, Gabriel Navarro, Pham Huu Tiep

We investigate a beautiful conjecture of T. Wilde on character values and element orders of finite groups. We reduce it to a statement on nearly simple groups that can be checked `…

math.GR2024

Non-congruence presentations of finite simple groups

William Y. Chen, Alexander Lubotzky, Pham Huu Tiep

We prove two results on some special generators of finite simple groups and use them to prove that every non-abelian finite simple group $S$ admits a non-congruence presentation (a…

math.RT2024

Tensor product Markov chains and Weil representations

Jason Fulman, Michael Larsen, Pham Huu Tiep

We obtain sharp bounds on the convergence rate of Markov chains on irreducible representations of finite general linear, unitary, and symplectic groups (in both odd and even charac…

math.GR2024

Representation growth of Fuchsian groups and modular forms

Michael Larsen, Jay Taylor, Pham Huu Tiep

Let $Γ$ be a cocompact, oriented Fuchsian group which is not on an explicit finite list of possible exceptions and $q$ a sufficiently large prime power not divisible by the order o…

math.GR2024

Finite groups whose real irreducible representations have unique dimensions

Thomas Breuer, Frank Calegari, Silvio Dolfi +2

We determine the finite groups whose real irreducible representations have different degrees.

math.GR2024

An extension of Gow's theorem

Robert M. Guralnick, Pham Huu Tiep

We extend Gow's theorem on products of semisimple regular conjugacy classes to finite groups whose generalized Fitting subgroup is Z(G)S where S is a quasisimple group of Lie type…

math.RT2024★ 1 cited

Uniform Character Bounds for Finite Classical Groups

Michael Larsen, Pham Huu Tiep

For every finite quasisimple group of Lie type $G$ , every irreducible character $χ$ of $G$ , and every element $g$ of $G$ , we give an exponential upper bound for the character ratio…

math.GR2024

Character estimates for finite classical groups and the asymptotic Thompson Conjecture

Michael Larsen, Pham Huu Tiep

If $G$ is a finite classical group, linear or unitary in any characteristic, and orthogonal in odd characteristic, we give an approximate formula for $χ (g)$ in which the error term…

math.GR2023

Finite simple characteristic quotients of the free group of rank 2

William Y. Chen, Alex Lubotzky, Pham Huu Tiep

In this paper we describe how to explicitly construct infinitely many finite simple groups as characteristic quotients of the rank 2 free group $F_{2}$ . This shows that a "baby" vers…

math.GR2023

Squares of Conjugacy Classes in Alternating Groups

Michael J. Larsen, Pham Huu Tiep

We extend to alternating groups $A_{n}$ several results about symmetric groups asserting that under various conditions on a conjugacy class, or more generally, a normal subset, $C$ o…

math.GR2023

The Field of Values of the Height Zero Characters

Gabriel Navarro, Lucas Ruhstorfer, Pham Huu Tiep +1

We determine what are the fields of values of the irreducible $p$ -height zero characters of all finite groups for $p = 2$ ; we conjecture what they should be for odd primes, and reduc…

math.RT2023

Symmetric Powers

János Kollár, Pham Huu Tiep

Given a faithful finite-dimensional representation $V$ of a finite group $G$ over any field $F$ , we show that any irreducible $F G$ -module $W$ appears, as a subm…

math.NT2023

The conjugation representation of the binary modular congruence group

Pham Huu Tiep

Motivated by the study of an Hecke action on iterated Shimura integrals undertaken in [H], in this appendix to [H] we prove that, for any prime $p \geq 5$ and for any integer $n \g…

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★ 1 cited

Brauer's Height Zero Conjecture

Gunter Malle, Gabriel Navarro, Amanda A. Schaeffer Fry +1

We complete the proof of Brauer's Height Zero Conjecture from 1955 by establishing the open implication for all odd primes.

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

Hall-Higman type theorems for exceptional groups of Lie type, I

Pham Huu Tiep, A. E. Zalesski

The paper studies the minimum polynomial degrees of $p$ -elements in cross-characteristic representations of simple groups of exceptional Lie type whose BN-pair rank is at most 2. S…

math.RT2021

Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements

Nguyen Ngoc Hung, Benjamin Sambale, Pham Huu Tiep

Let k(B_0) and l(B_0) respectively denote the number of ordinary and p-Brauer irreducible characters in the principal block B_0 of a finite group G. We prove that, if k(B_0)-l(B_0)…

math.GR2020★ 5 cited

Products of normal subsets and derangements

Michael Larsen, Aner Shalev, Pham Huu Tiep

In recent years there has been significant progress in the study of products of subsets of finite groups and of finite simple groups in particular. In this paper we consider which…

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…

math.RT2019

Irreducible restrictions of representations of alternating groups in small characteristics: Reduction theorems

Alexander Kleshchev, Lucia Morotti, Pham Huu Tiep

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for…

math.RT2018★ 7 cited

Lusztig Induction, Unipotent Supports, and Character Bounds

Jay Taylor, Pham H. Tiep

Recently, a strong exponential character bound has been established in [3] for all elements $g \in G^{F}$ of a finite reductive group $G^{F}$ which satisfy the condit…

math.RT2018

Brauer correspondent blocks with one simple module

Gabriel Navarro, Pam Huu Tiep, Carolina Vallejo

One of the main problems in representation theory is to understand the exact relationship between Brauer corresponding blocks of finite groups. The case where the local corresponde…

Degrees of p-rational characters and normality of Sylow p-subgroups

Zeros of characters and orders of elements in finite groups

Non-congruence presentations of finite simple groups

Tensor product Markov chains and Weil representations

Representation growth of Fuchsian groups and modular forms

Finite groups whose real irreducible representations have unique dimensions

An extension of Gow's theorem

Uniform Character Bounds for Finite Classical Groups

Character estimates for finite classical groups and the asymptotic Thompson Conjecture

Finite simple characteristic quotients of the free group of rank 2

Squares of Conjugacy Classes in Alternating Groups

The Field of Values of the Height Zero Characters

Symmetric Powers

The conjugation representation of the binary modular congruence group

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

Brauer's Height Zero Conjecture

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

Hall-Higman type theorems for exceptional groups of Lie type, I

Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements

Products of normal subsets and derangements

Character Levels and Character Bounds. II

Irreducible restrictions of representations of alternating groups in small characteristics: Reduction theorems

Lusztig Induction, Unipotent Supports, and Character Bounds

Brauer correspondent blocks with one simple module

Degrees of $p$ -rational characters and normality of Sylow $p$ -subgroups