We prove that the duality operator preserves the Frobenius–Schur indicators of characters of connected reductive groups of Lie type with connected center. This allows us to extend a result of D. Prasad which relates the Frobenius–Schur indicator of a regular real-valued character to its central character. We apply these results to compute the Frobenius–Schur indicators of certain real-valued, i...

A group G has a Frobenius graphical representation (GFR) if there is simple graph ? whose full automorphism isomorphic to acting on the vertices as group. In particular, any with GFR and Cayley graph. By very recent results of Spiga, exists function f such that finite complement H | > (| |) then admits GFR. This paper provides an infinite family graphs admit GFRs despite not meeting Spiga’s ...

We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley theorem for their invariants, and construct a Frobenius structure on their orbit spaces. This produces solutions F (t1, . . . , tn) of WDVV equations of associativity polynomial in t1, . . . , tn−1, exp tn.