Rhombic tilings and bott-samelson varieties

Laura Escobar, Oliver Pechenik, Bridget Eileen Tenner, Alexander Yong

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1921-1935
Number of pages15
JournalProceedings of the American Mathematical Society
Volume146
Issue number5
DOIs
StatePublished - Jan 1 2018

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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