科研之友
微信
新浪微博
Facebook
分享链接
摘要
Let F be a local field with finite residue field of characteristic p. Let G be a connected reductive group over F and B a minimal parabolic subgroup of G with Levi decomposition B = ZU. Let K be a special parahoric subgroup of G, in good position relative to (Z, U). Fix an absolutely irreducible smooth representation of K on a vector space V over some field C of characteristic p. Writing H(G, K, V) for the intertwining Hecke algebra of V in G, we define a natural algebra homomorphism from H(G, K, V) to H(Z, Z boolean AND K, V-U (boolean AND) (K)), we show it is injective and identify its image. We thus generalize work of F. Herzig, who assumed F of characteristic 0, G unramified and K hyperspecial, and took for C an algebraic closure of the prime field F-p. We show that in the general case H(G, K, V) need not be commutative; that is in contrast with the cases Herzig considers and with the more classical situation where V is trivial and the field of coefficients is the field of complex numbers.
- 出版日期2015-4
