Dissertation/Thesis Abstract

Affine Stanley symmetric functions for classical groups
by Pon, Steven A., Ph.D., University of California, Davis, 2010, 104; 3427426
Abstract (Summary)

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.

Indexing (document details)
Advisor: Schilling, Anne
Commitee: De Loera, Jesus, Vazirani, Monica
School: University of California, Davis
Department: Mathematics
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
Publication Number: 3427426
ISBN: 9781124316277