Abstract
S. Elnitsky (1997) gave an elegant bijection between rhombic tilings of 2n-gons and commutation classes of reduced words in the symmetric group on n letters. P. Magyar (1998) found an important construction of the Bott-Samelson varieties introduced by H. C. Hansen (1973) and M. Demazure (1974). We explain a natural connection between S. Elnitsky’s and P. Magyar’s results. This suggests using tilings to encapsulate Bott-Samelson data (in type A). It also indicates a geometric perspective on S. Elnitsky’s bijection. We also extend this construction by assigning desingularizations of Schubert varieties to the zonotopal tilings considered by B. Tenner (2006).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1921-1935 |
| Number of pages | 15 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 146 |
| Issue number | 5 |
| DOIs | |
| State | Published - Jan 1 2018 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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Escobar, L., Pechenik, O., Tenner, B. E., & Yong, A. (2018). Rhombic tilings and bott-samelson varieties. Proceedings of the American Mathematical Society, 146(5), 1921-1935. https://doi.org/10.1090/proc/13869