2026-09-21T20:26:34Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1269392026-06-17T14:44:06Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Roman Bezrukavnikov.
Yue, Guangyi.
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2020-09-03T16:42:20Z
2020-09-03T16:42:20Z
2020
2020
https://hdl.handle.net/1721.1/126939
1191267897
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
152 pages
eng
Massachusetts Institute of Technology
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
Mathematics.
Combinatorics of affine Springer fibers and combinatorial wall-crossing
Thesis
application/pdf
2020-09-03T16:42:15Z
Publication
Doctoral
Math
unknown
unknown
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