On the Existence and Irreducibility of Certain Series of Representations by Bertram Kostant

Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$

‎We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$‎. ‎We specialize the indeterminates used in defining these representations to non zero complex numbers‎. ‎We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$‎. ‎We then determine necessary and sufficient conditions that guarantee the irreducibility of th...

On Representations Associated with Symmetric Spaces by Bertram Kostant and Stephen Rallis

Root Systems for Levi Factors and Borel–de Siebenthal Theory

Let m be a Levi factor of a proper parabolic subalgebra q of a complex semisimple Lie algebra g. Let t = centm. A nonzero element ν ∈ t is called a t-root if the corresponding adjoint weight space gν is not zero. If ν is a t-root, some time ago we proved that gν is adm irreducible. Based on this result we develop in the present paper a theory of t-roots which replicates much of the structure of...

Lie Algebra Cohomology and the Representations Ofsemisimple Lie Groups

On Orbits Associated with Symmetric Spaces by Bertram Kostant and Stephen Rallis