This thesis introduces affine Stanley symmetric functions for the special orthogonal groups, a class of symmetric functions that model the cohomology of the affine Grassmannian, continuing the work of Lam and Lam, Schilling, and Shimozono on the special linear and symplectic groups, respectively. For the odd orthogonal groups, a Hopf-algebra isomorphism is given, identifying (co)homology Schubert classes with symmetric functions. For the even orthogonal groups, we conjecture an approximate model of (co)homology via symmetric functions, as an isomorphism is not possible. Additionally, Pieri rules for multiplication by special Schubert classes are given in both cases. We present a type-free interpretation of Pieri factors, used in the definition of affine Stanley symmetric functions for any classical type.
|Commitee:||De Loera, Jesus, Vazirani, Monica|
|School:||University of California, Davis|
|School Location:||United States -- California|
|Source:||DAI-B 71/12, Dissertation Abstracts International|
|Subjects:||Mathematics, Theoretical Mathematics|
|Keywords:||Classical groups, Combinatorics, Orthogonal groups, Pieri rules, Schubert classes, Symmetric functions|
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