Publication
On complete reducibility of tensor products of simple modules over simple algebraic groups
Publications associées (62)
Multiplicity-free Representations of Algebraic Groups
Donna Testerman, Martin W. Liebeck
Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...
Amer Mathematical Soc2024Cohomology in singular blocks of parabolic category O
We determine the dimensions of Ext -groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category O for complex semisimple Lie algebras and affine Kac-Moody algebras. ...
2023Almost cyclic regular semisimple elements in irreducible representations of simple algebraic groups
Let G be a simple linear algebraic group defined over an algebraically closed field of characteristic p ≥ 0 and let φ be a nontrivial p-restricted irreducible representation of G. Let T be a maximal torus of G and s ∈ T . We say that s is Ad-regular if α(s ...
2023Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity
Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...
EPFL2022Coxeter Combinatorics For Sum Formulas In The Representation Theory Of Algebraic Groups
Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...
AMER MATHEMATICAL SOC2022Multiplicity-free representations of algebraic groups II
Donna Testerman, Martin W. Liebeck
We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2022Spherical birational sheets in reductive groups
We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2021The algebra of Boolean matrices, correspondence functors, and simplicity
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...
2020A Distributed Cyber-Attack Detection Scheme With Application to DC Microgrids
Giancarlo Ferrari Trecate, Mustafa Sahin Turan
DC microgrids often present a hierarchical control architecture, requiring integration of communication layers. This leads to the possibility of malicious attackers disrupting the overall system. Motivated by this application, in this article, we present a ...
2020Simple and projective correspondence functors
A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. We determine exactly which simple correspondence functors are projective. We also determine which simple ...
2019