On the unitarizability of derived functor modules.
A connection between representation of compact groups and some invariant ensembles of hermitian matrices is described. We focus on two types of invariant ensembles which extend the gaussian and the Laguerre Unitary ensembles. We study them using projections and convolutions of invariant probability measures on adjoint orbits of a compact Lie group. These measures are described by semiclassical approximation involving tensor and restriction multiplicities. We show that a large class of them are determinantal....
Let be a preprojective algebra of type , and let be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories for an injective -module, and we introduce a mutation operation between complete rigid modules in . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to .
Let be the space of linear differential operators on weighted densities from to as module over the orthosymplectic Lie superalgebra , where , is the space of tensor densities of degree on the supercircle . We prove the existence and uniqueness of projectively equivariant quantization map from the space of symbols to the space of differential operators. An explicite expression of this map is also given.
Soient une variété algébrique complexe, lisse, irréductible, et deux espaces vectoriels complexes de dimension finie et un morphisme de dans l’espace Lin des applications linéaires de dans . Pour , on note et le noyau et l’image de , le morphisme de dans Lin qui associe à l’application linéaire . Soit i la dimension minimale de . On dit que ala propriété en si i est inférieur à i. Soient le dual de , S l’algèbre symétrique de , l’idéal de engendré par...