Recursive properties of branching and BGG resolution

TL;DR

This paper explores the recursive structure of branching coefficients and their role in constructing parabolic Verma modules, leading to generalized Weyl-Verma formulas and BGG resolution sequences.

Contribution

It introduces a novel approach using singular element decomposition to derive generalized Weyl-Verma formulas and connect branching coefficients with BGG resolutions.

Findings

Derived recursive relations for branching coefficients.

Constructed parabolic Verma modules using singular element decomposition.

Established links between branching coefficients and BGG resolution sequences.

Abstract

Recurrent relations for branching coefficients are based on a special type of singular element decomposition. We show that this decomposition can be used to construct the parabolic Verma modules and finally to obtain the generalized Weyl-Verma formulas for characters. We demonstrate how branching coefficients can determine the generalized BGG resolution sequence.