Let g = g0 ⊕ g1 be a simple Z2-graded Lie algebra and let b0 be a fixed Borel subalgebra of g0. We describe and enumerate the abelian b0-stable subalgebras of g1.

Let an affine Weyl group Ŵ act as a group of affine transformations on a real vector space V . We analyze the Ŵ -orbit of a regular element in V and deduce applications to Kostant’s formula for… (More)

We extend classical results of Kostant and al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted… (More)

We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial… (More)

Let g be a finite-dimensional semisimple Lie algebra and (· , ·) its Killing form, σ an elliptic automorphism of g, and a a σ-invariant reductive subalgebra of g, such that the restriction of the… (More)

This note is an exposition of old and recent results of B. Kostant regarding the relationships between the exterior algebra of a simple Lie algebra g and the action of the Casimir operator on it (see… (More)

Several very interesting results connecting the theory of abelian ideals of Borel subalgebras, some ideas of D. Peterson relating the previous theory to the combinatorics of affine Weyl groups, and… (More)

Let an affine Weyl group Ŵ act as a group of affine transformations on a real vector space V . We analyze the Ŵ -orbit of a regular element in V and deduce applications to Kostant’s formula for… (More)

Several very interesting results connecting the theory of abelian ideals of Borel subalgebras, some ideas of D. Peterson relating the previous theory to the combinatorics of affine Weyl groups, and… (More)