Correction to: Homological multiplicities in representation theory of p-adic groups

نویسندگان

چکیده

Regrettably, the paper [1] had two incorrect lemmas. Nevertheless, statements of theorems in are correct with no modification required. Specifically, [1, Lemma 6.4] does not hold for spherical spaces, and also conclusion B.2] is valid generality stated there. The effect error on proof Theorem 6.1] significant. In § 1 one we provide a that relay upon 6.4]. minor explain nessecary modifications §2.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

THE MOD p REPRESENTATION THEORY OF p-ADIC GROUPS

1.1. The p-adic numbers. A rational number x ∈ Q× may be uniquely written as x = ab p n with a, b and n nonzero integers such that p ab. We define ordp(x) = n, |x|p = p−n, |0|p = 0. |·|p defines an absolute value on Q, satisfying the stronger ultrametric triangle equality |x+ y|p ≤ max(|x|p, |y|p). We define Qp to be the completion Q with respect to this metric and we use the same notation | · ...

متن کامل

THE MOD p REPRESENTATION THEORY OF p - ADIC GROUPS

Exercise 1 (Maximal compact subgroups of G). A lattice in Qp is a finitelygenerated Zp-submodule of Qp that generates Qp as vector space. In particular, it’s free of rank n. Note that G acts transitively on the set of lattices in Qp . (i) Show that K = StabG(Zp ). (ii) Suppose that K ′ is a compact subgroup of G. Show that K ′ stabilises a lattice. (Hint: show that the K ′-orbit of Zp is finite...

متن کامل

Continuous representation theory of p-adic Lie groups

In this paper we give an overview over the basic features of the continuous representation theory of p-adic Lie groups as it has emerged during the last five years. The main motivation for developing such a theory is a possible extension of the local Langlands program to p-adic Galois representations. This is still very much in its infancy. But in the last section we will describe a first appro...

متن کامل

Representation theory of p-adic groups and canonical bases

In this paper, we interpret the Gindikin–Karpelevich formula and the Casselman–Shalika formula as sums over Kashiwara–Lusztig’s canonical bases, generalizing the results of Bump and Nakasuji (2010) [7] to arbitrary split reductive groups. We also rewrite formulas for spherical vectors and zonal spherical functions in terms of canonical bases. In a subsequent paper Kim and Lee (preprint) [14], w...

متن کامل

Homological Algebra for Schwartz Algebras of Reductive P-adic Groups

Let G be a reductive group over a non-Archimedean local field. Then the canonical functor from the derived category of smooth tempered representations of G to the derived category of all smooth representations of G is fully faithful. Here we consider representations on bornological vector spaces. As a consequence, if G is semi-simple, V and W are tempered irreducible representations of G, and V...

متن کامل

ذخیره 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: Mathematische Zeitschrift

سال: 2021

ISSN: ['1432-1823', '0025-5874']

DOI: https://doi.org/10.1007/s00209-021-02806-7