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Regular trace formula and base change for G L ( n )

Yuval Z. Flicker (1990)

Annales de l'institut Fourier

The “regular”trace formula, for a test function with a local component which is Iwahori-biinvariant and sufficiently regular with respect to the other components, is developed in the context of a reductive group. It is used to give a simple proof of the theory of base-change for cuspidal automorphic representations of G L ( n ) which have a supercuspidal component. A purely local proof is given to transfer orbital integrals of sufficiently many spherical functions, by relating them to regular Iwahori functions....

Towards the Jacquet conjecture on the Local Converse Problem for p -adic GL n

Dihua Jiang, Chufeng Nien, Shaun Stevens (2015)

Journal of the European Mathematical Society

The Local Converse Problem is to determine how the family of the local gamma factors γ ( s , π × τ , ψ ) characterizes the isomorphism class of an irreducible admissible generic representation π of GL n ( F ) , with F a non-archimedean local field, where τ runs through all irreducible supercuspidal representations of GL r ( F ) and r runs through positive integers. The Jacquet conjecture asserts that it is enough to take r = 1 , 2 , ... , n 2 . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture,...

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