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Permanent link (DOI): https://doi.org/10.7939/R3SQ8QS08

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T-Surfaces in the Affine Grassmannian Open Access

Descriptions

Other title
Subject/Keyword
affine Grassmannian
T-surface
attractive point
torus
T-orbit closure
Schubert variety
Peterson translate
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Cheng, Valerie
Supervisor and department
Kuttler, Jochen (Mathematical and Statistical Sciences)
Examining committee member and department
Penin, Alexander (Physics)
Chernousov, Vladimir (Mathematical and Statistical Sciences)
Pianzola, Arturo (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2010-10-01T15:36:56Z
Graduation date
2010-11
Degree
Master of Science
Degree level
Master's
Abstract
In this thesis we examine singularities of surfaces and affine Schubert varieties in the affine Grassmannian $\mathcal{G}/\mathcal{P}$ of type $A^{(1)}$, by considering the action of a particular torus $\widehat{T}$ on $\mathcal{G}/\mathcal{P}$. Let $\Sigma$ be an irreducible $\widehat{T}$-stable surface in $\mathcal{G}/\mathcal{P}$ and let $u$ be an attractive $\widehat{T}$-fixed point with $\widehat{T}$-stable affine neighborhood $\Sigma_u$. We give a description of the $\widehat{T}$-weights of the tangent space $T_u(\Sigma)$ of $\Sigma$ at $u$, give some conditions under which $\Sigma$ is nonsingular at $u$, and provide some explicit criteria for $\Sigma_u$ to be normal in terms of the weights of $T_u(\Sigma)$. We will also prove a conjecture regarding the singular locus of an affine Schubert variety in $\mathcal{G}/\mathcal{P}$.
Language
English
DOI
doi:10.7939/R3SQ8QS08
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
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