Orbital varieties in types $B$ and $C$

TL;DR

This paper corrects previous proofs and provides a parametrization of orbital varieties in types B and C Lie algebras using domino tableaux, also detailing how to compute these varieties from Weyl group elements.

Contribution

It offers a corrected proof and a new combinatorial parametrization of orbital varieties in types B and C Lie algebras, linking them to domino tableaux.

Findings

Corrected the main result proof from earlier work.

Parametrized orbital varieties using domino tableaux.

Provided a method to compute orbital varieties from Weyl group elements.

Abstract

We correct the proof of the main result of an earlier paper, parametrizing orbital varieties in a complex simple Lie algebra of type $B$ or $C$ in terms of domino tableaux and showing how to compute the orbital variety attached to an element of the Weyl group in either of these types.