# Regular trace formula and base change for $GL\left(n\right)$

Annales de l'institut Fourier (1990)

- Volume: 40, Issue: 1, page 1-30
- ISSN: 0373-0956

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topFlicker, Yuval Z.. "Regular trace formula and base change for $GL(n)$." Annales de l'institut Fourier 40.1 (1990): 1-30. <http://eudml.org/doc/74871>.

@article{Flicker1990,

abstract = {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 $GL(n)$ 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. Transfer of orbital integrals of smooth functions is not used in the proof. Instead it is obtained as a corollary to the local lifting.},

author = {Flicker, Yuval Z.},

journal = {Annales de l'institut Fourier},

keywords = {Hecke algebra; Satake transform; matching solid companions; admissible representations; base-change lifting; test function; cuspidal automorphic representations; regular Iwahori functions},

language = {eng},

number = {1},

pages = {1-30},

publisher = {Association des Annales de l'Institut Fourier},

title = {Regular trace formula and base change for $GL(n)$},

url = {http://eudml.org/doc/74871},

volume = {40},

year = {1990},

}

TY - JOUR

AU - Flicker, Yuval Z.

TI - Regular trace formula and base change for $GL(n)$

JO - Annales de l'institut Fourier

PY - 1990

PB - Association des Annales de l'Institut Fourier

VL - 40

IS - 1

SP - 1

EP - 30

AB - 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 $GL(n)$ 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. Transfer of orbital integrals of smooth functions is not used in the proof. Instead it is obtained as a corollary to the local lifting.

LA - eng

KW - Hecke algebra; Satake transform; matching solid companions; admissible representations; base-change lifting; test function; cuspidal automorphic representations; regular Iwahori functions

UR - http://eudml.org/doc/74871

ER -

## References

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