Generalized Harish-Chandra theory for unipotent characters of finite classical groups (Q1084505)

Let G be a finite general linear, unitary, symplectic or orthogonal group over the field \(F_ q\) (a ''classical'' group) and r a prime not dividing q. The authors show: ''There is an integer e and a polynomial \(\Phi (X)=X^ e\pm 1\) such that \(r| \Phi (q)\) and such that the following holds: To each unipotent character \(\rho\) there corresponds a pair (L,\(\Psi)\) (determined up to conjugacy), where L is a regular subgroup of G of the form a product of a classical group and a cyclic torus of order \(\Phi\) (q), \(\Psi\) is a unipotent character of L of degree divisible by the full power of r dividing \(| L:Z(L)|\) and \(\rho\) is a constituent of \(R^ G_ L(\Psi).''\) This result may be seen as an extension of the Harish-Chandra theory for these finite groups of Lie type. The result is extendable to arbitrary irreducible characters of classical groups.