Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/147864
Title: SIGNED PERMUTATION MODULES OF THE IWAHORI-HECKE ALGEBRA
Authors: LUO JIETONG
ORCID iD:   orcid.org/0000-0003-0742-460X
Keywords: Iwahori-Hecke algebra, symmetric group, signed permutation module, modular representation theory, Specht filtration, homomorphism space
Issue Date: 27-Jun-2018
Citation: LUO JIETONG (2018-06-27). SIGNED PERMUTATION MODULES OF THE IWAHORI-HECKE ALGEBRA. ScholarBank@NUS Repository.
Abstract: For the modular representation theory of Iwahori-Hecke algebra ℋ, in the past the theory for permutation modules M<sup>µ</sup> and pure signed modules N<sup>µ</sup> is built by the cellular bases of ℋ. According to these, we can give a generalization of both of these two kinds of modules, which at the same time is also the generalization of signed Young permutation module for the symmetric group, called the signed permutation modules. This thesis mainly introduces this kind of modules, and go on detailed study on the properties of this kind of modules. We generalize the results we have for the permutation modules and pure signed modules, and apply them to the signed permutation modules to understand the structure of this kind of modules, including the bases and the filtrations. Also, we will study the structure of the homomorphism modules for two signed permutation modules with some specific conditions required.
URI: http://scholarbank.nus.edu.sg/handle/10635/147864
Appears in Collections:Master's Theses (Open)

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