TY - JOUR
T1 - The local Langlands correspondence for inner forms of SL n
AU - Aubert, Anne Marie
AU - Baum, Paul
AU - Plymen, Roger
AU - Solleveld, Maarten
N1 - Funding Information:
The authors wish to thank Ioan Badulescu for interesting emails about the method of close fields, Wee Teck Gan for explaining some subtleties of inner forms and Guy Henniart for pointing out a weak spot in an earlier version of Theorem 4.4. We also thank the referee for his comments, which helped to clarify and improve the paper. Paul Baum was partially supported by NSF Grant DMS-1200475. Maarten Solleveld was partially supported by a NWO Vidi Grant No. 639.032.528.
Publisher Copyright:
© 2016, The Author(s).
PY - 2016/12/1
Y1 - 2016/12/1
N2 - Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group SL n(F). It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for SL n(F) enhanced with an irreducible representation of an S-group and, on the other hand, the union of the spaces of irreducible admissible representations of all inner forms of SL n(F) up to equivalence. An analogous result is shown in the archimedean case. For p-adic fields, this is based on the work of Hiraga and Saito. To settle the case where F has positive characteristic, we employ the method of close fields. We prove that this method is compatible with the local Langlands correspondence for inner forms of GL n(F) , when the fields are close enough compared to the depth of the representations.
AB - Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group SL n(F). It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for SL n(F) enhanced with an irreducible representation of an S-group and, on the other hand, the union of the spaces of irreducible admissible representations of all inner forms of SL n(F) up to equivalence. An analogous result is shown in the archimedean case. For p-adic fields, this is based on the work of Hiraga and Saito. To settle the case where F has positive characteristic, we employ the method of close fields. We prove that this method is compatible with the local Langlands correspondence for inner forms of GL n(F) , when the fields are close enough compared to the depth of the representations.
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U2 - 10.1186/s40687-016-0079-4
DO - 10.1186/s40687-016-0079-4
M3 - Article
AN - SCOPUS:85032888395
VL - 3
JO - Research in Mathematical Sciences
JF - Research in Mathematical Sciences
SN - 2522-0144
IS - 1
M1 - 32
ER -