On the classification of primitive ideals for complex classical Lie algebras, III
On the classification of the Lie algebras .
On the cohomology of nilpotent Lie algebras
On the cohomology of vector fields on parallelizable manifolds
In the present paper we determine for each parallelizable smooth compact manifold the second cohomology spaces of the Lie algebra of smooth vector fields on with values in the module . The case of is of particular interest since the gauge algebra of functions on with values in a finite-dimensional simple Lie algebra has the universal central extension with center , generalizing affine Kac-Moody algebras. The second cohomology classifies twists of the semidirect product of with the...
On the combinatorial Kashiwara-Vergne conjecture. (Sur la conjecture combinatoire de Kashiwara-Vergne.)
On the combinatorics of Kac's asymmetry function
We use categories to recast the combinatorial theory of full heaps, which are certain labelled partially ordered sets that we introduced in previous work. This gives rise to a far simpler set of definitions, which we use to outline a combinatorial construction of the so-called loop algebras associated to affine untwisted Kac--Moody algebras. The finite convex subsets of full heaps are equipped with a statistic called parity, and this naturally gives rise to Kac's asymmetry function. The latter is...
On the combinatorics of Young-Capelli symmetrizers.
On the complicatedness of the pair (g,K).
On the composition structure of the twisted Verma modules for
We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra , including the explicit structure of singular vectors for both and one of its Lie subalgebras , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as -modules on the Schubert cells in the full flag manifold for .
On the computation of Clebsch-Gordan coefficients and the dilation effect.
On the constructions of Tits and Faulkner: an isomorphism theorem.
On the definition of the dual Lie coalgebra of a Lie algebra.
Let L be a Lie algebra over a field K. The dual Lie coalgebra Lº of L has been defined by W. Michaelis to be the sum of all good subspaces V of the dual space L* of L: V is good if tm(V) ⊂ V ⊗ V, where m is the multiplication of L. We show that Lº = tm-1(L* ⊗ L*) as in the associative case.
On the degenerate multiplicity of the loop algebra for the 6V transfer matrix at roots of unity.
On the Demazure character formula
On the Demazure character formula II. Generic homologies
On the Derived Length of Solvable Lie Algebras.
On the double Poincaré series of the enveloping algebras of certain graded Lie algebras.
On the Enright-Varadarajan modules : a construction of the discrete series
On the exponential representation of .
On the formula of Ślebodziński for Lie derivative of tensor fields in a differential space