99 citations · 492 across the 111 of their papers we have counts for
20 papers · 1 filter
Invariant derivations and trace bounds
Skip Garibaldi, Robert M. Guralnick, Eric M. Rains
About 20 years ago, J-P.~Serre announced a bound on the trace of elements of compact Lie groups under the adjoint representation together with related results, provided indications…
Generic stabilizers for simple algebraic groups
Skip Garibaldi, Robert M. Guralnick
We prove a myriad of results related to the stabilizer in an algebraic group of a generic vector in a representation of over an algebraically closed field . Our resu…
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…
Sectional rank and Cohomology
Robert M. Guralnick, Pham Huu Tiep
We prove that there is a bound on the dimension of the first cohomology group of a finite group with coefficients in an absolutely irreducible in characteristic p in terms of the s…
Generically free representations III: extremely bad characteristic
Skip Garibaldi, Robert M. Guralnick
In parts I and II, we determined which faithful irreducible representations of a simple linear algebraic group are generically free for Lie(), i.e., which have an op…
Generically free representations II: irreducible representations
Skip Garibaldi, Robert M. Guralnick
We determine which faithful irreducible representations of a simple linear algebraic group are generically free for Lie(), i.e., which have an open subset consisting…
Generically free representations I: large representations
Skip Garibaldi, Robert M. Guralnick
For a simple linear algebraic group acting faithfully on a vector space and under mild assumptions, we show: if is large enough, then the Lie algebra of acts generi…
Character Levels and Character Bounds
Robert M. Guralnick, Michael Larsen, Pham Huu Tiep
We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of…
Globally Irreducible Weyl Modules for Quantum Groups
Skip Garibaldi, Robert M. Guralnick, Daniel K. Nakano
The authors proved that a Weyl module for a simple algebraic group is irreducible over every field if and only if the module is isomorphic to the adjoint representation for …
Globally Irreducible Weyl Modules
Skip Garibaldi, Robert M. Guralnick, Daniel K. Nakano
In the representation theory of split reductive algebraic groups, it is well known that every Weyl module with minuscule highest weight is irreducible over every field. Also, the a…
A lower bound for the dimension of a highest weight module
Daniel Goldstein, Robert Guralnick, Richard Stong
For each integer and each complex simple Lie algebra , we determine the least dimension of an irreducible highest weight representation of whose…
Adequate subgroups and indecomposable modules
Robert Guralnick, Florian Herzig, Pham Huu Tiep
The notion of adequate subgroups was introduced by Jack Thorne [59]. It is a weakening of the notion of big subgroups used by Wiles and Taylor in proving automorphy lifting theorem…
Adequate groups of low degree
Robert Guralnick, Florian Herzig, Pham Huu Tiep
The notion of adequate subgroups was introduced by Jack Thorne [42]. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving…
Reducibility of nilpotent commuting varieties
Robert M. Guralnick, Nham V. Ngo
Let be the set of nilpotent by matrices over an algebraically closed field . For each , let be the variety consisting of all pairwise commutin…
Adequate Subgroups II
Robert Guralnick
The notion of adequate subgroups was introduced by Jack Thorne. It is a weakening of the notion of big subgroup used by Wiles and Taylor in proving automorphy lifting theorems for…
Representation Growth in positive characteristic and conjugacy classes of maximal subgroups
Robert Guralnick, Michael Larsen, Pham Huu Tiep
We study the representation growth of alternating and symmetric groups in positive characteristic and restricted representation growth for the finite groups of Lie type. We show th…
Certain subgroups of Weyl groups are split
Daniel Goldstein, Robert Guralnick
Let C be the centralizer in a finite Weyl group of an elementary abelian 2-subgroup. We show that every complex representation of C can be realized over the field of rational numbe…
Low Degree Representations of Simple Lie Groups
Robert Guralnick, Michael Larsen, Corey Manack
We give upper bounds for the number of irreducible representations of dimension at most n for a compact semisimple Lie group. In particular, we prove that there are at most n irred…
GAP Computations Concerning Hamiltonian Cycles in the Generating Graphs of Finite Groups
Thomas Breuer
This is a collection of examples showing how the GAP system can be used to compute information about the generating graphs of finite groups. It includes all examples that were need…
Symmetric powers and a problem of Kollar and Larsen
Robert M. Guralnick, Pham Huu Tiep
We prove a conjecture of Kollar and Larsen on Zariski closed subgroups of which act irreducibly on some symmetric power with . This conjecture has in…