共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Let π be a cuspidal automorphic representation ofGL
2n
. We prove an identity between two spectral distributions onSp
2n
andGL
2n
respectively. The first is the spherical distribution with respect toSp
n×Sp
nof the residual Eisenstein series induced from π. The second is the weighted spherical distribution of π with respect toGL
n×GL
nand a certain degenerate Eisenstein series. A similar identity relates the pair (U
2n
,Sp
n) and (GL
n/E,GL
n/F) whereE/F is the quadratic extension defining the quasi-split unitary groupU
2n
. We also have a Whittaker version of these trace identities.
First-named author partially supported by NSF grant DMS 0070611.
Second-named author partially supported by NSF grant DMS 9970342. 相似文献
3.
In modern number theory there are famous theorems on the modularity of Dirichlet series attached to geometric or arithmetic
objects. There is Hecke’s converse theorem, Wiles proof of the Taniyama-Shimura conjecture, and Fermat’s Last Theorem to name
a few. In this article in the spirit of the Langlands philosophy we raise the question on the modularity of the GL2-twisted spinor L-function Z
G
⊗
h
(s) related to automorphic forms G,h on the symplectic group GSp2 and GL2. This leads to several promising results and finally culminates into a precise very general conjecture. This gives new insights
into the Miyawaki conjecture on spinor L-functions of modular forms. We indicate how this topic is related to Ramakrishnan’s
work on the modularity of the Rankin-Selberg L-series. 相似文献
4.
Boaz Tamir 《Israel Journal of Mathematics》1991,73(2):161-188
The ingredients of an “L-function machine” for the quasi-split groupU
n, n
+1 × Res GL
n
are treated here, following similar theories of P. Shapiro and S. Gelbart. We start with a known Rankin-Selberg type integral
having an Euler product. In section 2 we compute the local integral to get a localL function. This is done by working with an “L group” related to
L
G and the relative root system. All computations are carried out for the split and the non-split case. In section 3 we address
the problem of analytic continuation of the Eisenstein series. This involves computation of poles of intertwining operators. 相似文献
5.
We give a stratification of the GIT quotient of the Grassmannian G
2,n
modulo the normaliser of a maximal torus of SL
n
(k) with respect to the ample generator of the Picard group of G
2,n
. We also prove that the flag variety GL
n
(k)/B
n
can be obtained as a GIT quotient of GL
n+1(k)/B
n+1 modulo a maximal torus of SL
n+1(k) for a suitable choice of an ample line bundle on GL
n+1(k)/B
n+1.
Dedicated to Professor C De Concini on the occasion of his 60th birthday 相似文献
6.
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
7.
In this article we prove the Jacquet-Langlands local correspondence in non-zero characteristic. Let F be a local field of non-zero charactersitic and G′ an inner form of GLn(F); then, following [17], we prove relations between the representation theory of G′ and the representation theory of an inner form of GLn(L), where L is a local field of zero characteristic close to F. The proof of the Jacquet-Langlands correspondence between G′ and GLn(F) is done using the above results and ideas from the proof by Deligne, Kazhdan and Vignéras [10] of the zero characteristic case. We also get the following, already known in zero characteristic: orthogonality relations for G′, inequality involving conductor and level for representations of G′ and finiteness for automorphic cuspidal representations with fixed component at almost every place for an inner form of GLn over a global field of non-zero characteristic. 相似文献
8.
9.
Péter E. Frenkel 《Central European Journal of Mathematics》2006,4(2):242-249
We give formulae relating the value Xλ (g) of an irreducible character of a classical group G to entries of powers of the matrix g ε G. This yields a far-reaching generalization of a result of J.L. Cisneros-Molina concerning the GL
2 case [1].
Partially supported by OTKA grants T 042769 and T 046365 相似文献
10.
Given a permutation , construct a graph G
π on the vertex set {1, 2,..., n} by joining i to j if (i) i < j and π(i) < π(j) and (ii) there is no k such that i < k < j and π(i) < π(k) < π(j). We say that π is forest-like if G
π is a forest. We first characterize forest-like permutations in terms of pattern avoidance, and then by a certain linear map
being onto. Thanks to recent results of Woo and Yong, these show that forest-like permutations characterize Schubert varieties
which are locally factorial. Thus forest-like permutations generalize smooth permutations (corresponding to smooth Schubert
varieties).
We compute the generating function of forest-like permutations. As in the smooth case, it turns out to be algebraic. We then
adapt our method to count permutations for which G
π is a tree, or a path, and recover the known generating function of smooth permutations.
Received March 27, 2006 相似文献
11.
Min Ho Lee 《Monatshefte für Mathematik》2007,338(2):321-336
We introduce vector-valued Jacobi-like forms associated to a representation
r: G? GL(n,\Bbb C)\rho: \Gamma \rightarrow GL(n,{\Bbb C})
of a discrete subgroup
G ì SL(2,\Bbb C)\Gamma \subset SL(2,{\Bbb C})
in
\Bbb Cn{\Bbb C}^n
and establish a correspondence between such vector-valued Jacobi-like forms and sequences of vector-valued modular forms
of different weights with respect to ρ. We determine a lifting of vector-valued modular forms to vector-valued Jacobi-like
forms as well as a lifting of scalar-valued Jacobi-like forms to vector-valued Jacobi-like forms. We also construct Rankin-Cohen
brackets for vector-valued modular forms. 相似文献
12.
We develop a duality theory between the continuous representations of a compactp-adic Lie groupG in Banach spaces over a givenp-adic fieldK and certain compact modules over the completed group ringo
K[[G]]. We then introduce a “finiteness” condition for Banach space representations called admissibility. It will be shown that
under this duality admissibility corresponds to finite generation over the ringK[[G]]: =K ⊗o
K[[G]]. Since this latter ring is noetherian it follows that the admissible representations ofG form an abelian category. We conclude by analyzing the irreducibility properties of the continuous principal series of the
groupG: = GL2(ℤ
p
). 相似文献
13.
Let μ be a minuscule coweight for either GL
n
or GSp
2n
, and regard μ as an element t
μ in the extended affine Weyl group . We say that an element is μ-admissible if there exists μ′ in the Weyl group orbit of μ such that x≤t
μ′ in the Bruhat order on . Our main result is that is μ-admissible if and only if it is μ-permissible, where μ-permissibility is defined using inequalities arising naturally
in the study of bad reduction of Shimura varieties.
Received: 5 July 1999 相似文献
14.
We study the canonical forms and invariants of linear and bilinear control systems and the properties of orbits of these classes
of systems under similarity transformations, that is, the action of the group G = GL
n
(a change of coordinates in the state space) on the spaces of systems. 相似文献
15.
Given a graphG onn vertices and a total ordering ≺ ofV(G), the transitive orientation ofG associated with ≺, denotedP(G; ≺), is the partial order onV(G) defined by settingx<y inP(G; ≺) if there is a pathx=x
1
x
2…x
r=y inG such thatx
1 ≺x
j for 1≦i<j≦r. We investigate graphsG such that every transitive orientation ofG contains
2
n
−o(n
2) relations. We prove that almost everyG
n,p satisfies this requirement if
, but almost noG
n,p satisfies the condition if (pn log log logn)/(logn log logn) is bounded. We also show that every graphG withn vertices and at mostcn logn edges has some transitive orientation with fewer than
2
n
−δ(c)n
2 relations.
Partially supported by MCS Grant 8104854. 相似文献
16.
It is well known that every finite subgroup of GL
d
(Q
) is conjugate to a subgroup of GL
d
(Z
). However, this does not remain true if we replace general linear groups by symplectic groups. We say that G is a group of inertia type of G is a finite group which has a normal Sylow-p-subgroup with cyclic quotient. We show that if >d+1, and G is a subgroup of Sp
2d
(Q
) of inertia type, then G is conjugate in GL
2d
(Q
) to a subgroup of Sp
2d
(Z
). We give examples which show that the bound is sharp. We apply these results to construct, for every odd prime , isogeny classes of Abelian varieties all of whose polarizations have degree divisible by 2. We prove similar results for Euler characteristic of invertible sheaves on Abelian varieties over fields of positive characteristic. 相似文献
17.
Emília Draženská 《Mathematica Slovaca》2011,61(5):675-686
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. The
crossing numbers of G□C
n
for some graphs G on five and six vertices and the cycle C
n
are also given. In this paper, we extend these results by determining the crossing number of the Cartesian product G □ C
n
, where G is a specific graph on six vertices. 相似文献
18.
David Soudry 《Israel Journal of Mathematics》2000,120(1):511-561
In this paper we prove the full multiplicativity (in both variables) of gamma factors for generic representations of SO2ℓ+1 × GL
n
. These gamma factors are initially defined as proportionality factors of local functional equations, derived from a corresponding
global theory of certain Rankin-Selberg integrals which interpolate standardL-functions for SO2ℓ+1 × GL
n
. 相似文献
19.
Let K be a (algebraically closed ) field. A morphism A ⟼ g
−1
Ag, where A ∈ M(n) and g ∈ GL(n), defines an action of a general linear group GL(n) on an n × n-matrix space M(n), referred to as an adjoint action. In correspondence with the adjoint action is the coaction α: K[M(n)] → K[M(n)] ⊗ K[GL(n)] of a Hopf algebra K[GL(n)] on a coordinate algebra K[M(n)] of an n × n-matrix space, dual to the conjugation morphism. Such is called an adjoint coaction. We give coinvariants of an adjoint coaction
for the case where K is a field of arbitrary characteristic and one of the following conditions is satisfied: (1) q is not a root of unity; (2) char K = 0 and q = ±1; (3) q is a primitive root of unity of odd degree. Also it is shown that under the conditions specified, the category of rational
GL
q
× GL
q
-modules is a highest weight category. 相似文献
20.
The subgroups E(m,R) ⊗ E(n,R) ≤ H ≤ G = GL(mn,R) are studied under the assumption that the ring R is commutative and m, n ≥ 3. The group GL
m
⊗GL
n
is defined by equations, the normalizer of the group E(m,R) ⊗ E(n,R) is calculated, and with each intermediate subgroup H it is associated a uniquely determined lower level (A,B,C), where A,B,C are ideals in R such that mA,A
2 ≤ B ≤ A and nA,A
2 ≤ C ≤ A. The lower level specifies the largest elementary subgroup satisfying the condition E(m, n,R, A,B,C) ≤ H. The standard answer to this problem asserts that H is contained in the normalizer N
G
(E(m,n,R, A,B,C)). Bibliography: 46 titles. 相似文献