Abstract
Strong Gelfand pairs describe a relation between a group and a subgroup, using a relation between inner products of their characters. We find all strong Gelfand pairs of the dihedral and dicyclic groups, and several of the sporadic groups. We provide some results for the strong Gelfand pairs of the affine linear groups, in addition to the exceptional classical groups $\mathrm{Sp}_4(q)$ for $q$ a power of $2$.
Degree
MS
College and Department
Computational, Mathematical, and Physical Sciences; Mathematics
Rights
https://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Marrow, Joseph E., "Strong Gelfand Pairs of Some Finite Groups" (2024). Theses and Dissertations. 10475.
https://scholarsarchive.byu.edu/etd/10475
Date Submitted
2024-07-25
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd13313
Keywords
Gelfand pairs, strong Gelfand pairs, symplectic group, dihedral group, dicyclic group, sporadic group
Language
english