Abstract
We extend the notion of proper elements to all finite Coxeter groups. For all infinite families of finite Coxeter groups we prove that the probability a random element is proper goes to zero in the limit. This proves a conjecture of the third author and Alexander Yong regarding the proportion of Schubert varieties that are Levi spherical for all infinite families of Weyl groups. We also enumerate the proper elements in the exceptional Coxeter groups.
Original language | English (US) |
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Article number | 32 |
Journal | European Journal of Mathematics |
Volume | 10 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2024 |
Keywords
- 05E14
- 14M15
- 20P05
- Chernoff bounds
- Proper elements
- Schubert varieties
- Spherical varieties
ASJC Scopus subject areas
- General Mathematics