Geodesic
A crystal on decreasing factorizations in the 0-Hecke monoid
Jennifer Morse ; Jianping Pan ; Wencin Poh ; Anne Schilling1
1University of California at Davis
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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We introduce a type $A$ crystal structure on decreasing factorizations of fully-commu\-tative elements in the 0-Hecke monoid which we call $\star$-crystal. This crystal is a $K$-theoretic generalization of the crystal on decreasing factorizations in the symmetric group of the first and last author. We prove that under the residue map the $\star$-crystal intertwines with the crystal on set-valued tableaux recently introduced by Monical, Pechenik and Scrimshaw. We also define a new insertion from decreasing factorization to pairs of semistandard Young tableaux and prove several properties, such as its relation to the Hecke insertion and the uncrowding algorithm. The new insertion also intertwines with the crystal operators.
DOI : 10.37236/9168
Classification : 05E10, 05E05, 14N15, 20G42
Mots-clés : semistandard Young tableaux, Hecke insertion, uncrowding algorithm

Jennifer Morse    ; Jianping Pan    ; Wencin Poh    ; Anne Schilling  1

1 University of California at Davis 
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     title = {A crystal on decreasing factorizations in the {0-Hecke} monoid},
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Jennifer Morse; Jianping Pan; Wencin Poh; Anne Schilling. A crystal on decreasing factorizations in the 0-Hecke monoid. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/9168

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