Concept
Semisimple Lie algebra
Publications associées (114)
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 Soc2024Lie groups in the symmetric group: Reducing Ulam's problem to the simple case
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 Diego2023Almost 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 ...
2023Cohomology 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. ...
2023