Analogues of Alternating Sign Matrices for Arbitrary Weyl Groups

Student: Thurman Forrest benjamin

Educational Programme: Mathematics (Master)

Final Grade: 10

Year of Graduation: 2017

We study the MacNeille completion of Weyl groups under the Bruhat order, with a particular focus on An and Bn. This is inspired by Lascoux and Schutzenberger's result that the MacNeille completion of the Bruhat order on An Weyl groups is equinumerous with alternating sign matrices. We give another proof of this result and study the type Bn case in more detail. In particular we discover a set of inequalities characterizing ideals of bigrassmanians of type Bn, and show that relaxing one of the conditions gives us a bijection to half turn symmetric alternating sign matrices.

Full text (added June 3, 2017)

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