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Virginia Tech
The Combinatorial Curve Neighborhoods of Affine Flag Manifold in Type A<sub>n-1</sub><sup>(1)</sup>
Abstract
dc:description.abstractLet X be the affine flag manifold of Lie type A<sub>n-1</sub><sup>(1)</sup> where n ≥ 3 and let W<sub>aff</sub> be the associated affine Weyl group. The moment graph for X encodes the torus fixed points (which are elements of the affine Weyl group W<sub>aff</sub> and the torus stable curves in X. Given a fixed point u ∈ W<sub>aff</sub> and a degree d = (d₀, d₁, ..., d<sub>n−1</sub>) ∈ ℤ<sub>≥0</sub><sup>n</sup>, the combinatorial curve neighborhood is the set of maximal elements in the moment graph of X which can be reached from u′ ≤ u by a chain of curves of total degree ≤ d. In this thesis we give combinatorial formulas and algorithms for calculating these elements.
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2019
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Aslan, Songul
- Chair dc:contributor.committeechair
-
- Mihalcea, Constantin Leonardo
- Committee members dc:contributor.committeemember
-
- Orr, Daniel D.
- Shimozono, Mark M.
- Floyd, William J.
Subjects
dc:subject × 5Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:21133
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/93039