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Weak order on alternating sign matrix varieties
Algebra & Discrete Mathematics| Speaker: | Laura Escobar, UC Santa Cruz |
| Location: | 1147 MSB |
| Start time: | Tue, May 6 2025, 2:10PM |
Alternating sign matrices (ASMs) form the MacNeille completion of the strong Bruhat order on the symmetric group. An ASM variety is a generalized determinantal variety that is obtained by intersecting a collection of matrix Schubert varieties. ASM varieties are indexed by ASMs. There is a natural interpretation of the poset of ASMs as the containment order on ASM varieties. In 2018, Hamaker and Reiner defined weak Bruhat order on ASMs, which when restricted to the symmetric group, is the usual weak order. We initiate a geometric study of weak order on ASMs varieties, focusing on how combinatorial properties of this poset describe geometric properties of ASM varieties. This is joint work with Patricia Klein and Anna Weigandt.