Inverting the Satake map for Sp n and applications to Hecke operators
نویسندگان
چکیده
منابع مشابه
The Hecke category (part II—Satake equivalence)
Theorem 1. The convolution ∗ admits a commutativity constraint making Sph into a rigid tensor category. There exists a faithful, exact tensor “fiber” functor Sat : Sph → Vect inducing an equivalence (modulo a sign in the commutativity constraint) of Sph with Rep(G) as tensor categories, where G is the Langlands dual group of the reductive group G, whose weights are the coweights of G and vice v...
متن کاملThe Satake Isomorphism for Special Maximal Parahoric Hecke Algebras
Let G denote a connected reductive group over a nonarchimedean local field F . Let K denote a special maximal parahoric subgroup of G(F ). We establish a Satake isomorphism for the Hecke algebra HK of K-bi-invariant compactly supported functions on G(F ). The key ingredient is a Cartan decomposition describing the double coset space K\G(F )/K. We also describe how our results relate to the trea...
متن کاملHecke operators and the stable homology of GL(n)
Let R be a field of any characteristic and A a principal ideal domain. We make a conjecture that asserts that any Hecke operator T acts punctually on any Hecke eigenclass in the stable homology with trivial coefficients R of a principal congruence subgroup Γ in GL(n, A), i.e. as multiplication by the number of single cosets contained in T . In the case where A = Z, this conjecture implies that ...
متن کاملInverting the Hopf map
We calculate the η-localization of the motivic stable homotopy ring over C, confirming a conjecture of Guillou and Isaksen. Our approach is via the motivic Adams-Novikov spectral sequence. In fact, work of Hu, Kriz and Ormsby implies that it suffices to compute the α1localization of the classical Adams-Novikov E2-term, and this is what we do. Guillou and Isaksen also propose a pattern of differ...
متن کاملInverting the Frobenius Map
The famous Frobenius characteristic map is a bijection from the space of characters of a symmetric group S n to the space of homogeneous symmetric functions of degree n. In this note, we prove a formula for the inverse map. More precisely, we express the generating function for the values of an arbitrary virtual character of S n in terms of the symmetric function which is the Frobenius image of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2007
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-007-9035-7