Abstract
dc:description.abstractWe construct a strong filtered graph \Gammas(\Lambda) dependent on the dominant weight $\Lambda$, and a weak filtered graph \Gammaw(\Kcen) dependent on the canonical central element $\Kcen$ for an arbitrary Kac-Moody algebra $g$. In our construction, both graphs (\Gammas(\Lambda), \Gammaw(\Kcen)) have the vertex set as the Weyl group of $g$, with the grading given by the length function. The edges of the graph \Gammas(\La) are labeled versions of the $\lambda$-chain model of K-Chevalley rules for Kac-Moody flag manifolds as developed by Lenart and Shimozono, originally defined by Lenart and Postnikov. Meanwhile, the labels on \Gammaw(\Kcen) come from the dual multiplication map of K-cohomology of affine Grassmannian GrG. We conjecture that the strong filtered graph and weak filtered graph are dual, which means we get an identity when we apply the up and down operators on the vertices. We proved this identity except one case that where we call the chain is $j$-present. Our identity is similar to the Möbius construction of the dual filtered graph, as previously studied by Patrias and Pylyavskyy, and in fact, in the limit $n\rightarrow \infty$ of the A(1)n-1, our construction recovers their identity. We also expect to recover their combinatorics of Möbius deformation of the shifted Young's lattice in type C(1)n as $n$ approaches infinity.
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
- 2024
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Jiang, Shuai
- Chair dc:contributor.committeechair
-
- Shimozono, Mark M.
- Committee members dc:contributor.committeemember
-
- Orr, Daniel D.
- Yang, Yun
- Mihalcea, Constantin Leonardo
Subjects
dc:subject × 4Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:39984
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/118929