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arXiv · 1605.05613

Rhombic tilings and Bott-Samelson varieties

Laura Escobar·Oliver Pechenik·Bridget Eileen Tenner·Alexander Yong
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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 combinatorics. We also extend this construction by assigning desingularizations to the zonotopal tilings considered by B.~Tenner (2006).

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Laura Escobar, Oliver Pechenik, Bridget Eileen Tenner, Alexander Yong. 2016-05-18. Rhombic tilings and Bott-Samelson varieties. https://doi.org/10.1090/proc/13869

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