Regular representation on the big cell and big projective modules in the category O
Konstantin Styrkas
Abstract
We study the algebra of regular functions on the big cell of the Gauss decomposition of a simple complex Lie group G. We prove that it is spanned by the matrix elements of big projective modules in the BGG category O, and admits a decomposition of Peter-Weyl type. The subspace of Whittaker vectors in the regular representation on the big cell gives a realization of the big projective modules in O, similar to the Borel-Weil theorem. These results can be extended to the quantum groups.
Create a lesson
Related papers
On silting theory for complete path algebras
Maximilian Kaipel, Daniel Labardini-Fragoso, Håvard Utne Terland
Geometrization of Kottwitz-Shelstad transfer and Vogan's conjecture on local Arthur packets
Clifton Cunningham, Alexander Hazeltine, Baiying Liu et al.
Hammock coordinates for silting subcategories of derived-discrete algebras
Shantanu Sardar
Representations of Bound Quivers over F1 and Hall Algebras
Changjian Fu, Xuelian Xiao
Closed energy formulas on tensor squares of perfect crystals of types D4(3) and G2(1)
Shaolong Han
Generalized parabolic Demazure modules and the N!/2-conjecture for two-row diagrams
Anton Khoroshkin, Ievgen Makedonskyi