Classification of unipotent representations of simple p -adic groups

By G. Lusztig. 2001

211 citations recorded by the source corpus.

Let G(K) be the group of K-rational points of a connected adjoint simple algebraic group defined over a non-archimedean local field K. In this paper we classify the unipotent representations of G(K) in terms of the geometry of the Langlands dual group. (This was known earlier in the special case where G(K) is an inner form of a split group.) We also determine which representations are tempered or square integrable.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3a3de4c52494ec7130143937da13c942b49cf0ad

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In Algebra and Number Theory

1. Syu Kato
2. J. Arthur
3. E. Opdam
4. M. Solleveld
5. Mark Reeder
6. B. Gross
7. E. Sommers
8. George J. McNinch

In Discrete Mathematics and Combinatorics

1. Mark Reeder
2. M. Solleveld
3. B. Gross
4. J. Arthur
5. E. Opdam
6. George J. McNinch
7. Syu Kato
8. E. Sommers

In Mathematical Physics

1. M. Solleveld
2. Mark Reeder
3. Syu Kato
4. B. Gross
5. J. Arthur
6. E. Opdam
7. George J. McNinch
8. E. Sommers

Citations in the corpus

• Character sheaves on disconnected groups, X (2003, background): “The theory of character sheaves on G is also crucial for the classification of ”unipotent representations” of simple p-adic groups [ L5 ] and here one is forced to allow G to be disconnected if one wants to include p-adic groups that are not inner forms of split groups.”
• From Laplace to Langlands via representations of orthogonal groups (2006, background): “BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 43, Number 2, Pages 163–205 S 0273-0979(06)01100-1 Article electronically published on February 10, 2006”
• An exotic Deligne-Langlands correspondence for symplectic groups (2006, background): “[ Lu95a ]). However, there are many areas of mathematics which wait for the full-representation theory of Hecke algebras with unequal parameters (see e.g.”
• A Note on L-packets (2006, methodology): “7. If G is an adjoint group, a parametrization of certain packets ƒ` was established in [ Lu ].”
• Homological algebra for affine Hecke algebras (2007, methodology): “Ane Hecke algebras are useful tools in the study of the representation theory and harmonic analysis of a reductive p-adic group G, cf. [BuKu1, BuKu2, Lus3 , Mor1, Mor2].”
• Component groups of unipotent centralizers in good characteristic (2002, background): “S j (t) = 1g. Then the equality of Rt and RJ is proved in [ Lus95 , Lemma 5.4] (in loc.”
• Representations of Hecke Algebras at Roots of Unity (2011, unknown): “by Meinolf GECK Seminaire BOURBAKI 50eme annee, 1997-98, n° 836 Novembre 1997 Hecke algebras arise naturally in the representation theory of finite or p-adic Cheval-ley groups, as endomorphism algebras of certain induced representations (see Carter [9], Lusztig [44], and the references there).”