Lattice associated to a Shi variety

Nathan Chapelier-Laget

Lattice associated to a Shi variety

Combinatorics 2021-10-05 v2 Group Theory

Authors: Nathan Chapelier-Laget

Abstract

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

Keywords

weyl group affine weyl group shi variety irreducible components semidistributive lattice

Cite

@article{arxiv.2107.06220,
  title  = {Lattice associated to a Shi variety},
  author = {Nathan Chapelier-Laget},
  journal= {arXiv preprint arXiv:2107.06220},
  year   = {2021}
}

Comments

14 pages, 10 figures. arXiv admin note: text overlap with arXiv:2010.04310

Lattice associated to a Shi variety

Abstract

Keywords

Cite

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