Journal of Combinatorics

Volume 14 (2023)

Number 1

Lattice associated to a Shi variety

Pages: 1 – 20



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


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.


affine Weyl groups, Shi variety, irreducible components

2010 Mathematics Subject Classification

Primary 06B99. Secondary 20F55.

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