Journal of Combinatorics

Volume 14 (2023)

Number 1

Lattice associated to a Shi variety

Pages: 1 – 20

DOI: https://dx.doi.org/10.4310/JOC.2023.v14.n1.a1

Author

Nathan Chapelier-Laget (LACIM, Université du Québec à Montréal, Canada)

Abstract

Let $W$ be an irreducible Weyl group and Wa its affine Weyl group. In [4] the author defined an affine variety $\hat{X}_{W_a}$, called the Shi variety of $W_a$, whose integral points are in bijection with $W_a$. The set of irreducible components of $\hat{X}_{W_a}$, denoted $H^0 (\hat{X}_{W_a})$, is of some interest and we show in this article that $H^0 (\hat{X}_{W_a})$ has a structure of a semi-distributive lattice.

Keywords

affine Weyl groups, Shi variety, irreducible components

2010 Mathematics Subject Classification

Primary 06B99. Secondary 20F55.

The full text of this article is unavailable through your IP address: 18.225.98.39

This work was partially supported by NSERC grants and by the LACIM at Université du Québec à Montréal.

Received 12 March 2021

Accepted 28 September 2021

Published 19 August 2022