The twist for Richardson varieties
Representation Theory
2022-10-11 v2 Algebraic Geometry
Combinatorics
Abstract
We construct the twist automorphism of open Richardson varieties inside the flag variety of a complex semisimple algebraic group. We show that the twist map preserves totally positive parts, and prove a Chamber Ansatz formula for it. Our twist map generalizes the twist maps previously constructed by Berenstein-Fomin-Zelevinsky, Marsh-Scott, and Muller-Speyer. We use it to explain the relationship between the two conjectural cluster structures for Richardson varieties studied by Leclerc and by Ingermanson.
Keywords
Cite
@article{arxiv.2204.05935,
title = {The twist for Richardson varieties},
author = {Pavel Galashin and Thomas Lam},
journal= {arXiv preprint arXiv:2204.05935},
year = {2022}
}
Comments
37 pages, 4 figures; v2: bibliography updates