Hecke Algebras of Classical Groups over p-adic Fields II

Wiley - Tập 127 - Trang 117-167 - 2001
Ju-Lee Kim1
1Department of Mathematics, University of Michigan, Ann Arbor, U.S.A.

Tóm tắt

In the previous part of this paper, we constructed a large family of Hecke algebras on some classical groups G defined over p-adic fields in order to understand their admissible representations. Each Hecke algebra is associated to a pair (J Σ, ρΣ) of an open compact subgroup J Σ and its irreducible representation ρΣ which is constructed from given data Σ = (Γ, P′0, ϱ). Here, Γ is a semisimple element in the Lie algebra of G, P′0 is a parahoric subgroup in the centralizer of Γ in G, and ϱ is a cuspidal representation on the finite reductive quotient of P′0. In this paper, we explicitly describe those Hecke algebras when P′0 is a minimal parahoric subgroup, ϱ is trivial and ρΣ is a character.

Tài liệu tham khảo

[BT] Bruhat, F. and Tits, J.: Groupes rçductifs sur un corps local I, Publ.Math. IHES 41 (1972), 1–251.

[BK1] Bushnell, C. and Kutzko, P.: The Admissible Dual of GL(N) via Compact Open Subgroups, Ann. Math Stud. 129, Princeton Univ. Press, 1993.

[BK2] Bushnell, C. and Kutzko, P.: Smooth representations of reductive p-adic groups: Structure theory via types, Proc. London Math. Soc. 77 (1998), 582–634.

[G] Goldstein, D.: Hecke algebra isomorphisms for tamely ramified characters, PhD thesis, U. Chicago (1990).

[HM1] Howe, R. (with collaboration of A. Moy): Harish-Chandra Homomorphisms for p-adic Groups, CBMS Regional Conf. Ser. 59, Amer. Math. Soc., Providence, RI, 1985.

[HM2] Howe, R. and Moy, A.: Hecke algebra isomorphisms for GL(n) over a p-adic field, J. Algebra 131 (1990), 388–424.

[IR] Ireland, K. and Rosen, M.: Classical Introduction to Modern Number Theory, 2nd edn, Springer-Verlag, New York, 1990.

[IM] Iwahori, N. and Matsumoto, H.: On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. IHES 25 (1965), 5–48.

[K1] Kim, J.-L.: Hecke algebras of classical groups over p-adic fields and supercuspidal representations, Amer. J. Math. 121 (1999), 967–1029.

[K2] Kim, J.-L.: Hecke algebras of classical groups over p-adic fields III Preprint 1998.

[L] Lusztig, L.: Classification of unipotent representations of simple p-adic groups, IMRN 11 (1995), 517–589.

[Mo] Morris, L.: Tamely ramified intertwining algebras, Invent. Math. 114 (1994), 1–54.

[My1] Moy, A.: Representations of U(2, 1) over a p-adic field, J. Reine. Angew. Math. 372 (1986), 178–208.

[My2] Moy, A.: Representations of GSp 4 over a p-adic field I, II, Compositio Math. 66 (1988), 237–284, 285-328.

[R] Roche, A.: Types and Hecke Algebras for principal series representations of split reductive p-adic groups, Ann. Sci. École Norm. Sup. (4) 31 (1998), 361–413.

[S] Shalika, J.: Representations of two by two unimodular groups over local fields, Preprint.

[T] Tits, J.: Reductive groups over local fields, Proc. Sympos. Pure Math. 33 (1979), 29–69.

Thông tin
Thông tin xuất bản

Wiley

Tập 127

117-167

Thông tin tác giả