Weights of Semiregular Nilpotents in Simple Lie Algebras of D Type

TL;DR

This paper calculates the weights of the adjoint action of semiregular sl_2-triples in simple D_n Lie algebras, advancing understanding of their structure through induction methods.

Contribution

It introduces a method to compute weights of semiregular sl_2-triples specifically in D_n type Lie algebras, providing new insights into their representation theory.

Findings

Computed weights for semiregular sl_2-triples in D_n Lie algebras

Established an induction-based approach for these calculations

Enhanced understanding of the algebraic structure of D_n Lie algebras

Abstract

We compute the weights of the adjoint action of semiregular $sl_2$-triples in simple Lie algebras of type $D_n$ using mathematical induction.