Naslov
Bigrassmannian permutations and Verma modules

Autori
Ko, Hankyung ; Mazorchuk, Volodymyr ; Mrđen, Rafael

Izvornik
Selecta mathematica, New series (1022-1824) 27 (2021); 55, 24

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Bigrassmannian permutations ; Verma modules ; BGG category O

Sažetak
We show that bigrassmannian permutations determine the socle of the cokernel of an inclusion of Verma modules in type A. All such socular constituents turn out to be indexed by Weyl group elements from the penultimate two- sided cell. Combinatorially, the socular constituents in the cokernel of the inclusion of a Verma module indexed by w∈S_n into the dominant Verma module are shown to be determined by the essential set of w and their degrees in the graded picture are shown to be computable in terms of the associated rank function. As an application, we compute the first extension from a simple module to a Verma module.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA