Gauss sums and supercuspidal representations of \(\mathrm{GL}_ n\). (English) Zbl 0718.11062
Representation theory and number theory in connection with the local Langlands conjecture, Proc. Conf., Augsburg/FRG 1985, Contemp. Math. 86, 215-224 (1989).
[For the entire collection see Zbl 0656.00012.]
The author looks at finite-dimensional central simple \(F\)-algebras \(A\) (where \(F\) is a \(p\)-adic field), from the perspective of the (not quite complete) generalization that the Godement-Jacquet functional equation provides of Tate’s functional equation (for quasi-characters of \(F^*\)) to irreducible representations of \(F^*\).
The author looks at finite-dimensional central simple \(F\)-algebras \(A\) (where \(F\) is a \(p\)-adic field), from the perspective of the (not quite complete) generalization that the Godement-Jacquet functional equation provides of Tate’s functional equation (for quasi-characters of \(F^*\)) to irreducible representations of \(F^*\).
Reviewer: Richard A. Mollin (Calgary)
MSC:
| 11S45 | Algebras and orders, and their zeta functions |
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
