共查询到20条相似文献,搜索用时 78 毫秒
1.
Let F be a non-Archimedean local field and D a central F-division algebra of dimension n2, n?1. We consider first the irreducible smooth representations of D× trivial on 1-units, and second the indecomposable, n-dimensional, semisimple, Weil-Deligne representations of F which are trivial on wild inertia. The sets of equivalence classes of these two sorts of representations are in canonical (functorial) bijection via the composition of the Jacquet-Langlands correspondence and the Langlands correspondence. They are also in canonical bijection via explicit parametrizations in terms of tame admissible pairs. This paper gives the relation between these two bijections. It is based on analysis of the discrete series of the general linear group GLn(F) in terms of a classification by extended simple types. 相似文献
2.
Dipendra Prasad 《manuscripta mathematica》2000,102(2):263-268
We prove that the germ expansion of a discrete series representation π′ on GL
n
(D) where D is a division algebra over k of index m and the germ expansion of the representation π of GL
mn
(k) associated to π′ by the Deligne–Kazhdan–Vigneras correspondence are closely related, and therefore certain coefficients in the germ expansion
of a discrete series representation of GL
mn
(k) can be interpreted (and therefore sometimes calculated) in terms of the dimension of a certain space of (degenerate) Whittaker
models on GL
n
(D).
Received: 30 September 1999 / Revised version: 11 February 2000 相似文献
3.
We prove, over a p-adic local field F, that an irreducible supercuspidal representation of GL2n
(F) is a local Langlands functorial transfer from SO2n+1(F) if and only if it has a nonzero Shalika model (Corollary 5.2, Proposition 5.4 and Theorem 5.5). Based on this, we verify
(Sect. 6) in our cases a conjecture of Jacquet and Martin, a conjecture of Kim, and a conjecture of Speh in the theory of
automorphic forms. 相似文献
4.
Let F be either or . Consider the standard embedding and the action of GLn(F) on GLn+1(F) by conjugation. We show that any GLn(F)-invariant distribution on GLn+1(F) is invariant with respect to transposition. We prove that this implies that for any irreducible admissible smooth Fréchet
representations π of GLn+1(F) and of GLn(F),
. For p-adic fields those results were proven in [AGRS].
相似文献
5.
In this paper, we set up the general formulation to study distinguished residual representations of a reductive group G by the relative trace formula approach. This approach simplifies the argument of [JR], which deals with this type of relative
trace formula for a special symmetric pair (GL(2n), Sp(2n)) and also works for non-symmetric, spherical pairs. To illustrate our idea and method, we complete our relative trace formula
(both the geometric side identity and the spectral side identity) for the case (G
2, SL(3)).
Received: 6 February 1999 相似文献
6.
Christophe Breuil 《Compositio Mathematica》2003,138(2):165-188
Let p be a prime number and F a complete local field with residue field of characteristic p. In 1993, Barthel and Livné proved the existence of a new kind of
-representations of GL2(F) that they called 'supersingular' and on which one knows almost nothing. In this article, we determine all the supersingular representations of GL2(Q
p
) with their intertwinings. This classification shows a natural bijection between the set of isomorphism classes of supersingular representations of GL2(Q
p
) and the set of isomorphism classes of two-dimensional irreducible
-representations of
. 相似文献
7.
Alexandru Ioan Badulescu 《Inventiones Mathematicae》2008,172(2):383-438
In this paper we generalize the local Jacquet-Langlands correspondence to all unitary irreducible representations. We prove
the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong
multiplicity one Theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Mœglin–Waldspurger
and Jacquet–Shalika for GL(n). 相似文献
8.
Anne-Marie Aubert Uri Onn Amritanshu Prasad Alexander Stasinski 《Israel Journal of Mathematics》2010,175(1):391-420
We define a new notion of cuspidality for representations of GL
n
over a finite quotient o
k
of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups G
λ
of torsion o-modules. When n is a prime, we show that this notion of cuspidality is equivalent to strong cuspidality, which arises in the construction
of supercuspidal representations of GL
n
(F). We show that strongly cuspidal representations share many features of cuspidal representations of finite general linear
groups. In the function field case, we show that the construction of the representations of GL
n
(o
k
) for k ≥ 2 for all n is equivalent to the construction of the representations of all the groups G
λ
. A functional equation for zeta functions for representations of GL
n
(o
k
) is established for representations which are not contained in an infinitesimally induced representation. All the cuspidal
representations for GL4(o2) are constructed. Not all these representations are strongly cuspidal. 相似文献
9.
10.
Let F be a non-Archimedean locally compact field, and let p be its residual characteristic. Put G=GL
p
(F) and let G
′=D
×, where $D$ is a division algebra with centre F and of degree p
2 over F. The Jacquet–Langlands correspondence is a bijection between the discrete series of G and that of G
′. We describe this explicitly, in terms of Carayol's parametrization of these discrete series.
Received: 25 November 1999 相似文献
11.
Oded Yacobi 《Selecta Mathematica, New Series》2010,16(4):819-855
Branching of symplectic groups is not multiplicity free. We describe a new approach to resolving these multiplicities that
is based on studying the associated branching algebra B{\mathcal{B}}. The algebra B{\mathcal{B}} is a graded algebra whose components encode the multiplicities of irreducible representations of Sp
2n–2 in irreducible representations of Sp
2n
. Our first theorem states that the map taking an element of Sp
2n
to its principal n × (n + 1) submatrix induces an isomorphism of B{\mathcal{B}} to a different branching algebra B¢{\mathcal{B}^{\prime}}. The algebra B¢{\mathcal{B}^{\prime}} encodes multiplicities of irreducible representations of GL
n–1 in certain irreducible representations of GL
n+1. Our second theorem is that each multiplicity space that arises in the restriction of an irreducible representation of Sp
2n
to Sp
2n–2 is canonically an irreducible module for the n-fold product of SL
2. In particular, this induces a canonical decomposition of the multiplicity spaces into one-dimensional spaces, thereby resolving
the multiplicities. 相似文献
12.
Florian Herzig 《Inventiones Mathematicae》2011,186(2):373-434
Let F be a finite extension of ℚ
p
. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} to be supersingular. We then give the classification of irreducible admissible smooth GL
n
(F)-representations over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel–Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses. 相似文献
13.
Let X be a smooth complex projective variety with Neron–Severi group isomorphic to ℤ, and D an irreducible divisor with normal crossing singularities. Assume 1<r≤ 3. We prove that if π1(X) doesn't have irreducible PU(r) representations, then π1(X- D) doesn't have irreducible U(r) representations. The proof uses the non-existence of certain stable parabolic bundles. We also obtain a similar result for
GL(2) when D is smooth.
Received: 20 December 1999 / Revised version: 7 May 2000 相似文献
14.
15.
Let F be a non-Archimedean local field of residual characteristic two and let d be an odd positive integer. Let D be a central F-division algebra of dimension d
2. Let π be one of: an irreducible smooth representation of D
× , an irreducible cuspidal representation of GL
d
(F), an irreducible smooth representation of the Weil group of F of dimension d. We show that, in all these cases, if π is self-contragredient then it is defined over
\mathbb Q{\mathbb Q} and is orthogonal. We also show that such representations exist. 相似文献
16.
Oleg T. Izhboldin 《manuscripta mathematica》2000,102(1):41-52
Let F be a field of characteristic ≠2 and φ be a quadratic form over F. By X
φ we denote the projective variety given by the equation φ=0. For each positive even integer d≥8 (except for d=12) we construct a field F and a pair φ, ψ of anisotropic d-dimensional forms over F such that the Chow motives of X
φ and X
ψ coincide but . For a pair of anisotropic (2
n
-1)-dimensional quadrics X and Y, we prove that existence of a rational morphism Y→X is equivalent to existence of a rational morphism Y→X.
Received: 27 September 1999 / Revised version: 27 December 1999 相似文献
17.
《Quaestiones Mathematicae》2013,36(3-4):289-302
Abstract Let d be a positive integer and F be a field of characteristic 0. Suppose that for each positive integer n, I n is a polynomial invariant of the usual action of GLn (F) on Λd(Fn), such that for t ? Λd(F k) and s ? Λd(F l), I k + l (t l s) = I k(t)I t (s), where t ⊥ s is defined in §1.4. Then we say that {In} is an additive family of invariants of the skewsymmetric tensors of degree d, or, briefly, an additive family of invariants. If not all the In are constant we say that the family is non-trivial. We show that in each even degree d there is a non-trivial additive family of invariants, but that this is not so for any odd d. These results are analogous to those in our paper [3] for symmetric tensors. Our proofs rely on the symbolic method for representing invariants of skewsymmetric tensors. To keep this paper self-contained we expound some of that theory, but for the proofs we refer to the book [2] of Grosshans, Rota and Stein. 相似文献
18.
We extend Prasad’s results on the existence of trilinear forms on representations of GL
2 of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional
irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic
cohomology of the product of two modular curves constructed by Beilinson.
Received February 24, 2000 / final version received September 12, 2000?Published online November 8, 2000 相似文献
19.
In the present paper, we characterize ⋀n(GL(n, R)) over any commutative ring R as the connected component of the stabilizer of the Plücker ideal. This folk theorem is
classically known for algebraically closed fields and should also be well known in general. However, we are not aware of any
obvious reference, so we produce a detailed proof, which follows a general scheme developed by W.C.Waterhouse. The present
paper is a technical preliminary to a subsequent paper, where we construct the decomposition of transvections in polyvector
representations of GL
n. Bibliography: 50 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 338, 2006, pp. 69–97. 相似文献
20.
We study a family of complex representations of the group GL n (𝔬), where 𝔬 is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL n (F) to its maximal compact subgroup GL n (𝔬). We compute explicitly the transition matrix between a geometric basis of the Hecke algebra associated with the representation and an algebraic basis that consists of its minimal idempotents. The transition matrix involves combinatorial invariants of lattices of submodules of finite 𝔬-modules. The idempotents are p-adic analogs of the multivariable Jacobi polynomials. 相似文献