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Department Colloquium

Fri., Feb. 3, 2023 3:30 p.m.

Location: RIC 208

Speaker: Venkata Raghu Tej Pantangi, University of Regina

Title:  Cameron–Liebler Sets in Permutation Groups (518 kB) PDF file


Let G Sn be a transitive permutation group. Given i,j ∈ [n] ={1, ...,  n}, denote by xij the characteristic function of the set

{g : g (i ) = j }.

A Cameron–Liebler set (CL set) in G is a set which is represented by a Boolean function in the linear span of {xij : (i ,j) ∈ [n]2}. These are analogous to Boolean degree 1 functions on the hypercube and to Cameron–Liebler line classes in PG(3,q). Sets of the form {g : g (i ) ∈ X} and {g : i g (X)} (for i ∈ [n] and X ⊂ [n]) are canonically occurring examples of CL sets. A result of Ellis et al. shows that all CL sets in Sn are canonical.

In this talk, we will demonstrate many examples with “exotic” CL sets. Of special interest is an exotic CL set in PSL(2; q) with q ≡ 3 (mod 4), a 2-transitive group, just like Sn. The talk is based on ongoing joint work with Jozefien D’haeseleer and Karen Meagher.