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Educational Programme
Final Grade
Year of Graduation
Forrest benjamin Thurman
Analogues of Alternating Sign Matrices for Arbitrary Weyl Groups
(Master’s programme)
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.

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