TY - JOUR
T1 - Geometric structure in smooth dual and local Langlands conjecture
AU - Aubert, Anne Marie
AU - Baum, Paul
AU - Plymen, Roger
AU - Solleveld, Maarten
N1 - Funding Information:
The second author was partially supported by NSF grant DMS-0701184.
Publisher Copyright:
© 2014, The Mathematical Society of Japan and Springer Japan.
PY - 2014/9/1
Y1 - 2014/9/1
N2 - This expository paper first reviews some basic facts about p-adic fields, reductive p-adic groups, and the local Langlands conjecture. If G is a reductive p-adic group, then the smooth dual of G is the set of equivalence classes of smooth irreducible representations of G. The representations are on vector spaces over the complex numbers. In a canonical way, the smooth dual is the disjoint union of subsets known as the Bernstein components. According to a conjecture due to ABPS (Aubert–Baum–Plymen–Solleveld), each Bernstein component has a geometric structure given by an appropriate extended quotient. The paper states this ABPS conjecture and then indicates evidence for the conjecture, and its connection to the local Langlands conjecture.
AB - This expository paper first reviews some basic facts about p-adic fields, reductive p-adic groups, and the local Langlands conjecture. If G is a reductive p-adic group, then the smooth dual of G is the set of equivalence classes of smooth irreducible representations of G. The representations are on vector spaces over the complex numbers. In a canonical way, the smooth dual is the disjoint union of subsets known as the Bernstein components. According to a conjecture due to ABPS (Aubert–Baum–Plymen–Solleveld), each Bernstein component has a geometric structure given by an appropriate extended quotient. The paper states this ABPS conjecture and then indicates evidence for the conjecture, and its connection to the local Langlands conjecture.
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U2 - 10.1007/s11537-014-1267-x
DO - 10.1007/s11537-014-1267-x
M3 - Article
AN - SCOPUS:84907690197
SN - 0289-2316
VL - 9
SP - 99
EP - 136
JO - Japanese Journal of Mathematics
JF - Japanese Journal of Mathematics
IS - 2
ER -