Combinatorics of affine Springer fibers and combinatorial wall-crossing
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
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| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2020
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| Online Access: | https://hdl.handle.net/1721.1/126939 |
| _version_ | 1826204216555732992 |
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| author | Yue, Guangyi. |
| author2 | Roman Bezrukavnikov. |
| author_facet | Roman Bezrukavnikov. Yue, Guangyi. |
| author_sort | Yue, Guangyi. |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 |
| first_indexed | 2024-09-23T12:50:43Z |
| format | Thesis |
| id | mit-1721.1/126939 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T12:50:43Z |
| publishDate | 2020 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1269392020-09-04T03:23:33Z Combinatorics of affine Springer fibers and combinatorial wall-crossing Yue, Guangyi. Roman Bezrukavnikov. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 Cataloged from the official PDF of thesis. Includes bibliographical references (pages 149-152). This thesis deals with several combinatorial problems in representation theory. The first part of the thesis studies the combinatorics of affine Springer fibers of type A. In particular, we give an explicit description of irreducible components of Fl[subscript tS] and calculate the relative positions between two components. We also study the lowest two-sided Kazhdan-Lusztig cell and establish a connection with the affine Springer fibers, which is compatible with the affine matrix ball construction algorithm. The results also prove a special case of Lusztig's conjecture. The work in this part include joint work with Pablo Boixeda. In the second part, we define the combinatorial wall-crossing transformation and the generalized column regularization on partitions and prove that a certain composition of these two transformations has the same effect on the one-row partition. This result gives a special situation where column regularization, can be used to understand the complicated Mullineux map, and also proves a special case of Bezrukavnikov's conjecture. Furthermore, we prove a condition under which the two maps are exactly the same, generalizing the work of Bessenrodt, Olsson and Xu. The combinatorial constructions is related to the Iwahori-Hecke algebra and the global crystal basis of the basic [ ... ]-module and we provide several conjectures regarding the q-decomposition numbers and generalizations of results due to Fayers. This part is a joint work with Panagiotis Dimakis and Allen Wang. by Guangyi Yue. Ph. D. Ph.D. Massachusetts Institute of Technology, Department of Mathematics 2020-09-03T16:42:20Z 2020-09-03T16:42:20Z 2020 2020 Thesis https://hdl.handle.net/1721.1/126939 1191267897 eng MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided. http://dspace.mit.edu/handle/1721.1/7582 152 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Yue, Guangyi. Combinatorics of affine Springer fibers and combinatorial wall-crossing |
| title | Combinatorics of affine Springer fibers and combinatorial wall-crossing |
| title_full | Combinatorics of affine Springer fibers and combinatorial wall-crossing |
| title_fullStr | Combinatorics of affine Springer fibers and combinatorial wall-crossing |
| title_full_unstemmed | Combinatorics of affine Springer fibers and combinatorial wall-crossing |
| title_short | Combinatorics of affine Springer fibers and combinatorial wall-crossing |
| title_sort | combinatorics of affine springer fibers and combinatorial wall crossing |
| topic | Mathematics. |
| url | https://hdl.handle.net/1721.1/126939 |
| work_keys_str_mv | AT yueguangyi combinatoricsofaffinespringerfibersandcombinatorialwallcrossing |