Date/heure
13 juin 2024
15:45 - 16:45
Oratrice ou orateur
Marco Matassa (Oslo Met)
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
We consider the problem of quantizing the positive nilradical of a complex semisimple Lie algebra of finite rank, together with a certain fixed direct sum decomposition. The decompositions we consider are in one-to-one correspondence with total orders on the simple roots, and exhibit the nilradical as a direct sum of graded modules for appropriate Levi factors. We show that this situation can be quantized equivariantly as a finite-dimensional subspace within the positive part of the corresponding quantized enveloping algebra. Furthermore, we show that such subspaces give rise to left coideals, with the possible exception of components corresponding to some exceptional Lie algebras, and this property singles them out uniquely. Finally, we discuss how to use these quantizations to construct covariant first-order differential calculi on quantum flag manifolds, which coincide with those introduced by Heckenberger-Kolb in the irreducible case.