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math.CO2023
Subexpressions and the Bruhat order for double cosets
Ben Elias, Hankyung Ko, Nicolas Libedinsky +1
The Bruhat order on a Coxeter group is often described by examining subexpressions of a reduced expression. We prove that an analogous description applies to the Bruhat order on do…
math.RT2023
Demazure operators for double cosets
Ben Elias, Hankyung Ko, Nicolas Libedinsky +1
For any Coxeter system, and any double coset for two standard parabolic subgroups, we introduce a Demazure operator. These operators form a basis for morphism spaces in a category…
math.RT2023
Atoms and charge in type
Leonardo Patimo, Jacinta Torres
We construct atomic decompositions for crystals of type and define a charge statistic on them, thus providing positive combinatorial formulas for Kostka-Foulkes polynomials…