Methods for Finding Gelfand Pairs in Finite Groups with an Emphasis on Symmetry
DOI:
https://doi.org/10.22401/Keywords:
Gelfand pairs, , symmetric, weakly symmetric, multiplicity-free representations, GAPAbstract
This paper seeks to develop a procedure to identify all pairs within a finite group that are Gelfand, symmetric, and weakly symmetric. With the focus on the projective special linear groups. This leads to a unique class of "strictly weakly symmetric pairs." For the specific case of the projective special linear group PSL(2, p) where p is prime in the range , it is observed that only a single such pair exists.
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