Concept

Simple Lie group

Publications associées (124)

Multiplicity-free Representations of Algebraic Groups

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 Soc2024

Weyl metallic state induced by helical magnetic order

Henrik Moodysson Rønnow, Jan Hugo Dil, Ivica Zivkovic, Jian Rui Soh, Xupeng Yang

In the rapidly expanding field of topological materials there is growing interest in systems whose topological electronic band features can be induced or controlled by magnetism. Magnetic Weyl semimetals, which contain linear band crossings near the Fermi ...

Berlin2024

Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

Nicolas Monod

Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...

San Diego2023

Almost cyclic regular semisimple elements in irreducible representations of simple algebraic groups

Donna Testerman

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 ...

2023

Cohomology in singular blocks of parabolic category O

Jonathan Gruber

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. ...

2023

Lie groups as permutation groups: Ulam's problem in the nilpotent case

Nicolas Monod

Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...

WALTER DE GRUYTER GMBH2022

Eigenvalue multiplicities of group elements in irreducible representations of simple linear algebraic groups

Ana-Maria Retegan

Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimensional kG-module. For an element g of G we denote by $V_{g}( ...

EPFL2022

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

Jonathan Gruber

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 ...

EPFL2022

On minimal tilting complexes in highest weight categories

Jonathan Gruber

We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of complex simple Lie ...

2022

Assessment of metal-based dihydrofolate reductase inhibitors on a novel mesofluidic platform

Paul Joseph Dyson, Sarah Alexandra Pais Pereira

A new miniaturized micro sequential injection coupled with the lab-on-valve (mu SIA-LOV) technique was full-blown to perform inhibitory studies on dihydrofolate reductase (DHFR). The system was used to evaluate the DHFR inhibition activity of metal-based a ...

ELSEVIER SCIENCE SA2022

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