共查询到20条相似文献,搜索用时 31 毫秒
1.
M. Monastyrsky 《Proceedings of the Steklov Institute of Mathematics》2011,275(1):284-289
I discuss two related subjects: (1) Hecke surfaces and k-regular graphs, (2) duality transformations for lattice spin models. Each of them is related to deep mathematical and physical
theories, and at first glance, they have nothing in common. However, it became evident in recent years that there exist deep
internal relations between these two problems. Especially interesting (and mysterious) is the role of Hecke groups in this
context. I consider the following relevant example: Hecke graphs and Ramanujan graphs. 相似文献
2.
Udo Baumgartner James Foster Jacqueline Hicks Helen Lindsay Ben Maloney Iain Raeburn 《代数通讯》2013,41(11):4135-4147
Abstract We describe the Hecke algebra ?(Γ,Γ0) of a Hecke pair (Γ,Γ0) in terms of the Hecke pair (N,Γ0) where N is a normal subgroup of Γ containing Γ0. To do this, we introduce twisted crossed products of unital *-algebras by semigroups. Then, provided a certain semigroup S ? Γ/N satisfies S ?1 S = Γ/N, we show that ? (Γ,Γ0) is the twisted crossed product of ? (N,Γ0) by S. This generalizes a recent theorem of Laca and Larsen about Hecke algebras of semidirect products. 相似文献
3.
Kirsten Bremke 《manuscripta mathematica》1994,83(1):331-346
The purpose of this paper is to calculate the decomposition numbers for Hecke algebras of typeF
4 (andC
3) with unequal parameters. The problem is reduced to specifying decomposition maps of the generic Hecke algebras. The concept
of Kazhdan-Lusztig polynomials and left cells serves to determine their irreducible representations. We also prove a result
about the minimal ring over which the irreducible representations of the generic algebras can be realized. 相似文献
4.
This paper classifies the simple modules of the cyclotomic Hecke algebras of type G(r,1,n) and the affine Hecke algebras of type A in arbitrary characteristic. We do this by first showing that the simple modules of the cyclotomic Hecke algebras are indexed
by the set of “Kleshchev multipartitions”.
Received July 24, 1998; in final form February 8, 1999 相似文献
5.
A. Sankaranarayanan 《Lithuanian Mathematical Journal》2006,46(4):459-474
We improve the existing upper bound for the quantity |∑
n⩽x
a(n
2)|, where a(n
2) is the n
2th Hecke eigenvalue of a normalized holomorphic cusp form (Hecke eigenform) of the full modular group SL(2, ℤ), whenever the weight of the original holomorphic cusp form (Hecke eigenform) lies in a certain range.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 565–583, October–December, 2006. 相似文献
6.
Let P be a simple lattice polytope. We define an action of the Hecke operators on E(P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E(P). We also describe how the Brion–Vergne formula for E(P) transforms under the Hecke operators for nonsingular lattice polytopes P.
相似文献
7.
Sebahattin Ikikardes Recep Sahin I. Naci Cangul 《Bulletin of the Brazilian Mathematical Society》2009,40(4):479-494
In this paper, first, we determine the quotient groups of the Hecke groups H(λ
q
), where q ≥ 7 is prime, by their principal congruence subgroups H
p
(λ
q
) oflevel p, where p is also prime. We deal with the case of q = 7 separately, because of its close relation with the Hurwitz groups. Then, using the obtained results, we find the principal
congruence subgroups of the extended Hecke groups $
\overline H
$
\overline H
(λ
q
) for q ≥ 5 prime. Finally, we show that some of the quotient groups of the Hecke group H(λ
q
) and the extended Hecke group $
\overline H
$
\overline H
(λ
q
), q ≥ 5 prime, by their principal congruence subgroups H
p
(λ
q
) are M*-groups. 相似文献
8.
In this paper we prove a nonvanishing theorem for central values of L-functions associated to a large class of algebraic Hecke characters of CM number fields. A key ingredient in the proof is
an asymptotic formula for the average of these central values. We combine the nonvanishing theorem with work of Tian and Zhang
[TiZ] to deduce that infinitely many of the CM abelian varieties associated to these Hecke characters have Mordell–Weil rank zero.
Included among these abelian varieties are higher-dimensional analogues of the elliptic
\mathbb Q{{\mathbb Q}} -curves A(D) of B. Gross [Gr]. 相似文献
9.
Ken Ono 《Advances in Mathematics》2011,(1):527
The theory of congruences for the partition function p(n) depends heavily on the properties of half-integral weight Hecke operators. The subject has been complicated by the absence of closed formulas for the Hecke images P(z)|T(?2), where P(z) is the relevant modular generating function. We obtain such formulas using Euler?s Pentagonal Number Theorem and the denominator formula for the Monster Lie algebra. As a corollary, we obtain congruences for certain powers of Ramanujan?s Delta-function. 相似文献
10.
Thomas Keilen 《代数通讯》2013,41(5):1921-1926
For a Coxeter system (G, S) the multi-parametric alternating subalgebra H +(G) of the Hecke algebra and the alternating subgroup ?+(G) of the braid group are defined. Two presentations for H +(G) and ?+(G) are given; one generalizes the Bourbaki presentation for the alternating subgroups of Coxeter groups, another one uses generators related to edges of the Coxeter graph. 相似文献
11.
Özden Koruoğlu Recep Sahin Sebahattin İkikardes Ismail Naci Cangül 《Algebras and Representation Theory》2010,13(2):219-230
Let λ ≥ 2 and let H(λ) be the Hecke group associated to λ. Also let H(λ)\U be the Riemann surface associated to the Hecke group H(λ). In this article, we study the even subgroup H
e
(λ) and the power subgroups H
m
(λ) of the Hecke groups H(λ). We also study some genus 0 normal subgroups of finite index of H(λ). Finally, we discuss free normal subgroups of H(λ). 相似文献
12.
Steen Ryom-Hansen 《Journal of Algebraic Combinatorics》2011,33(1):57-79
We consider the algebra ℰ
n
(u) introduced by Aicardi and Juyumaya as an abstraction of the Yokonuma–Hecke algebra. We construct a tensor space representation
for ℰ
n
(u) and show that this is faithful. We use it to give a basis of ℰ
n
(u) and to classify its irreducible representations. 相似文献
13.
Michel van Meer 《Selecta Mathematica, New Series》2011,17(1):183-221
The bispectral quantum Knizhnik–Zamolodchikov (BqKZ) equation corresponding to the affine Hecke algebra H of type A
N-1 is a consistent system of q-difference equations which in some sense contains two families of Cherednik’s quantum affine Knizhnik–Zamolodchikov equations
for meromorphic functions with values in principal series representations of H. In this paper, we extend this construction of BqKZ to the case where H is the affine Hecke algebra associated with an arbitrary irreducible reduced root system. We construct explicit solutions
of BqKZ and describe its correspondence to a bispectral problem involving Macdonald’s q-difference operators. 相似文献
14.
We explain how the Bloch-Kato conjecture leads us to the following conclusion: a large prime dividing a critical value of the L-function of a classical Hecke eigenform f of level 1, should often also divide certain ratios of critical values for the standard L-function of a related genus two (and in general vector-valued) Hecke eigenform F. The relation between f and F (Harder?s conjecture in the vector-valued case) is a congruence involving Hecke eigenvalues, modulo the large prime. In the scalar-valued case we prove the divisibility, subject to weak conditions. In two instances in the vector-valued case, we confirm the divisibility using elaborate computations involving special differential operators. These computations do not depend for their validity on any unproved conjecture. 相似文献
15.
Wen-Ching Winnie Li 《Journal of Number Theory》2008,128(7):1941-1965
In this paper, we study the Drinfeld cusp forms for Γ1(T) and Γ(T) using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the cusp forms for Γ1(T) of small weights and conclude that these Hecke operators are simultaneously diagonalizable. We also show that the Hecke operators are not diagonalizable in general for Γ1(T) of large weights, and not for Γ(T) even of small weights. The Hecke eigenvalues on cusp forms for Γ(T) with small weights are determined and the eigenspaces characterized. 相似文献
16.
Pär Kurlberg 《Annales Henri Poincare》2007,8(1):75-89
We study extreme values of desymmetrized eigenfunctions (so called Hecke eigenfunctions) for the quantized cat map, a quantization
of a hyperbolic linear map of the torus. In a previous paper it was shown that for prime values of the inverse Planck’s constant
N = 1/h, such that the map is diagonalizable (but not upper triangular) modulo N, the Hecke eigenfunctions are uniformly bounded. The purpose of this paper is to show that the same holds for any prime N provided that the map is not upper triangular modulo N. We also find that the supremum norms of Hecke eigenfunctions are ≪ε Nε for all ε > 0 in the case of N square free.
Submitted: March 6, 2006; Accepted: April 30, 2006 相似文献
17.
Shi-Chao Chen 《Discrete Mathematics》2011,(12):940
Let ped(n) be the number of partitions of n wherein even parts are distinct (and odd parts are unrestricted). We obtain many congruences for ped(n)mod2 and mod4 by the theory of Hecke eigenforms. 相似文献
18.
David Carlton 《manuscripta mathematica》2001,105(2):201-234
We study the moduli surface for pairs of elliptic curves together with an isomorphism between their N-torsion groups. The Weil pairing gives a “determinant” map from this moduli surface to (Z/N
Z)*; its fibers are the components of the surface. We define spaces of modular forms on these components and Hecke correspondences
between them, and study how those spaces of modular forms behave as modules for the Hecke algebra. We discover that the component
with determinant −1 is somehow the “dominant” one; we characterize the difference between its spaces of modular forms and
the spaces of modular forms on the other components using forms with complex multiplication. In addition, we prove Atkin–Lehner-style
results about these spaces of modular forms. Finally, we show some simplifications that arise when N is prime, including a complete determination of such CM-forms, and give numerical examples.
Received: 20 September 2000 / Revised version: 7 February 2001 相似文献
19.
The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A
construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving
explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed
by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist
algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well
as complex reflection groups.
Received: July 25, 2001 相似文献
20.
Sinéad Lyle 《代数通讯》2013,41(5):1723-1752
We determine the v-decomposition numbers d μλ(v) for μ a partition with at most three parts. We use this information to compute the composition factors of the Specht modules of the Hecke algebra ?0 = ??, ω( n ) which correspond to partitions with at most three parts. 相似文献