Regular irreducible representations of classical groups over finite quotient rings

On certain supercuspidal representations of $SL_n(F)$ associated with tamely ramified extensions: the formal degree conjecture and the root number conjecture

“…The section 2 is devoted to the construction of the supercuspidal representation π β,θ of SL n (F ). After recalling, in the subsection 2.1, the general theory of the regular irreducible representations of the finite group G(O F /p r F ) (r ≥ 2) given by [18], we will define the irreducible unitary representation δ β,θ of SL n (O F ) in the subsection 2.2. The construction of the supercuspidal representation π β,θ is given in the subsection 2.3.…”

“…) and let us denote by Ω the set of the equivalence classes of the irreducible complex representations of G(O F /p l ′ ) correspond to Ω. Then [18] gives a parametrization of Ω as follows:…”

“…Then main result shown in [18], under the assumptions of Theorem 2.1.1, is that there exists a group homomorphism (not unique)…”

“…(see the subsection 2.2 for the precise definitions). We have the irreducible representation δ β,θ by the general theory given by [18].…”

On certain supercuspidal representations of symplectic groups associated with tamely ramified extensions : the formal degree conjecture and the root number conjecture

“…(see the subsection 2.2 for the precise definitions). We have the irreducible representation δ β,θ by the general theory given by [17].…”