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1.
If
is a complex simple Lie algebra, and k does not exceed the dual Coxeter number of
, then the absolute value of the kth coefficient of the
power of the Euler product may be given by the dimension of a subspace of
defined by all abelian subalgebras of
of dimension k. This has implications for all the coefficients of all the powers of the Euler product. Involved in the main results are Dale Petersons 2rank theorem on the number of abelian ideals in a Borel subalgebra of
, an element of type and my heat kernel formulation of Macdonalds -function theorem, a set Dalcove of special highest weights parameterized by all the alcoves in a Weyl chamber (generalizing Young diagrams of null m-core when
), and the homology and cohomology of the nil radical of the standard maximal parabolic subalgebra of the affine Kac–Moody Lie algebra. 相似文献
2.
Xiong Ping DAI 《数学学报(英文版)》2006,22(1):301-310
Let (X, G(X), m) be a probability space with a-algebra G(X) and probability measure m. The set V in G is called P-admissible, provided that for any positive integer n and positive-measure set Vn∈ contained in V, there exists a Zn∈G such that Zn belong to Vn and 0 〈 m(Zn) 〈 1/n. Let T be an ergodic automorphism of (X, G) preserving m, and A belong to the space of linear measurable symplectic cocycles 相似文献
3.
Let G be a connected Lie group, with Lie algebra
. In 1977, Duflo constructed a homomorphism of
-modules
, which restricts to an algebra isomorphism on invariants. Kashiwara and Vergne (1978) proposed a conjecture on the Campbell-Hausdorff
series, which (among other things) extends the Duflo theorem to germs of bi-invariant distributions on the Lie group G.
The main results of the present paper are as follows. (1) Using a recent result of Torossian (2002), we establish the Kashiwara–Vergne
conjecture for any Lie group G. (2) We give a reformulation of the Kashiwara–Vergne property in terms of Lie algebra cohomology. As a direct corollary,
one obtains the algebra isomorphism
, as well as a more general statement for distributions. 相似文献
4.
In our previous work, we introduced a bijection between the elements of the crystal base of the negative (resp. positive)
part of the quantized universal enveloping algebra
of a Kac–Moody algebra
that are fixed by a diagram automorphism and the elements of the crystal base of the negative (resp. positive) part of the
quantized universal enveloping algebra
of the orbit Lie algebra
of
. In this paper, we prove that this bijection commutes with the *-operation. As an application of this result we show that
there exists a canonical bijection between the elements ℬ0(λ) of the crystal base ℬ(λ) of an extremal weight module of extremal weight λ over
that are fixed by a diagram automorphism and the elements of the crystal base
of an extremal weight module of extremal weight
over
, if the crystal graph of
is connected.
Presented by P. Littelmann
Mathematics Subject Classifications (2000) Primary: 17B37, 17B10; secondary: 81R50. 相似文献
5.
Kazem Khashyarmanesh 《Archiv der Mathematik》2007,88(5):413-418
Let (
) be a commutative Noetherian local ring with non-zero identity,
an ideal of R and M a finitely generated R-module with
. Let D(–) := Hom
R
(–, E) be the Matlis dual functor, where
is the injective hull of the residue field
. We show that, for a positive integer n, if there exists a regular sequence
and the i-th local cohomology module H
i
a
(M) of M with respect to
is zero for all i with i > n then
The author was partially supported by a grant from Institute for Studies in Theoretical Physics and Mathematics (IPM) Iran
(No. 85130023).
Received: 9 August 2006 相似文献
6.
Tatsuo Nishitani 《Annali dell'Universita di Ferrara》2006,52(2):395-430
Abstract The well posedness of the Cauchy problem for the operator P=Dt2–Dxa(t,x)nDx,
with data on t=0 is studied assuming a ∈ CN(
(R)), s0>1 and sufficiently close to 1, a(t,x)≥ 0. Well posedness is proved in Gevrey classes γ(s), for
, n≥ n0.
Keywords: Partial differential equations, Cauchy problem, Well posedness 相似文献
7.
We generalize the notions of F-regular and F-pure rings to pairs
of rings R and ideals
with real exponent t>0, and investigate these properties. These F-singularities of pairs correspond to singularities of pairs of arbitrary codimension in birational geometry. Via this correspondence, we prove a sort of Inversion of Adjunction of arbitrary codimension, which states that for a pair (X,Y) of a smooth variety X and a closed subscheme
, if the restriction (Z,Y|Z) to a normal -Gorenstein closed subvariety
is klt (resp. lc), then the pair (X,Y+Z) is plt (resp. lc) near Z. 相似文献
8.
Sorin Popa 《Inventiones Mathematicae》2006,165(2):369-408
We consider crossed product II1 factors
, with G discrete ICC groups that contain infinite normal subgroups with the relative property (T) and σ trace preserving actions
of G on finite von Neumann algebras N that are “malleable” and mixing. Examples are the actions of G by Bernoulli shifts (classical and non-classical) and by Bogoliubov shifts. We prove a rigidity result for isomorphisms of
such factors, showing the uniqueness, up to unitary conjugacy, of the position of the group von Neumann algebra L(G) inside M. We use this result to calculate the fundamental group of M,
, in terms of the weights of the shift σ, for
and other special arithmetic groups. We deduce that for any subgroup S⊂ℝ+* there exist II1 factors M (separable if S is countable or S=ℝ+*) with
. This brings new light to a long standing open problem of Murray and von Neumann. 相似文献
9.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
and acting in spaces Lp(X, μ), where X is a compact topological space, φk∈C(X), φ = (φk)k=1N∈C(X)N, and
are linear positive operators (Ukf≥ 0 for f≥ 0). We consider the spectral exponent ln r(Aφ) as a functional depending on vector-function φ. We prove that ln r(Aφ) is continuous and on a certain subspace
of C(X)N is also convex. This yields that the spectral exponent is the Fenchel-Legendre transform of a convex functional
defined on a set
of continuous linear positive and normalized functionals on the subspace
of coefficients φ that is
相似文献
10.
Let E be a non empty set, let P : = E × E,
:= {x × E|x ∈ E},
:= {E × x|x ∈ E}, and
:= {C ∈ 2
P
|∀X ∈
: |C ∩ X| = 1} and let
. Then the quadruple
resp.
is called chain structure resp. maximal chain structure. We consider the maximal chain structure
as an envelope of the chain structure
. Particular chain structures are webs, 2-structures, (coordinatized) affine planes, hyperbola structures or Minkowski planes.
Here we study in detail the groups of automorphisms
,
,
,
related to a maximal chain structure
. The set
of all chains can be turned in a group
such that the subgroup
of
generated by
the left-, by
the right-translations and by ι the inverse map of
is isomorphic to
(cf. (2.14)). 相似文献
11.
Rolf Farnsteiner 《Inventiones Mathematicae》2006,166(1):27-94
Given an algebraically closed field k of characteristic p≥3, we classify the finite algebraic k-groups whose algebras of measures afford a principal block of tame representation type. The structure of such a group
is largely determined by a linearly reductive subgroup scheme
of SL(2), with the McKay quiver of
relative to its standard module being the Gabriel quiver of the principal block
. The graphs underlying these quivers are extended Dynkin diagrams of type
or
, and the tame blocks are Morita equivalent to generalizations of the trivial extensions of the radical square zero tame hereditary
algebras of the corresponding type. 相似文献
12.
If E is a separable symmetric sequence space with trivial Boyd indices and
is the corresponding ideal of compact operators, then there exists a C1-function fE, a self-adjoint element
and a densely defined closed symmetric derivation δ on
such that
, but
相似文献
13.
Abstract We examine the cut-off resolvent Rχ(λ) = χ (–ΔD – λ2)–1χ, where ΔD is the Laplacian with Dirichlet boundary condition and
equal to 1 in a neighborhood of the obstacle K. We show that if Rχ(λ) has no poles for
, then
This estimate implies a local energy decay. We study the spectrum of the Lax-Phillips semigroup Z(t) for trapping obstacles having at least one trapped ray.
Keywords: Trapping obstacles, Resonances, Local energy decay, Cut-off resolvent 相似文献
14.
Thomas Scanlon 《Inventiones Mathematicae》2006,163(1):191-211
We prove a p-adic version of the André-Oort conjecture for subvarieties of the universal abelian varieties. Let g and n be integers with n≥3 and p a prime number not dividing n. Let R be a finite extension of
, the ring of Witt vectors of the algebraic closure of the field of p elements. The moduli space
of g-dimensional principally polarized abelian varieties with full level n-structure as well as the universal abelian variety
over
may be defined over R. We call a point
R-special if
is a canonical lift and ξ is a torsion point of its fibre. Employing the model theory of difference fields and work of Moonen
on special subvarieties of
, we show that an irreducible subvariety of
containing a dense set of R-special points must be a special subvariety in the sense of mixed Shimura varieties. 相似文献
15.
Let
be an algebraically closed field and let
be an n-dimensional affine variety. Assume that f1,...,fk are polynomials which have no common zeros on X. We estimate the degrees of polynomials
such that 1=∑ki=1Aifi on X. Our estimate is sharp for k≤n and nearly sharp for k>n. Now assume that f1,...,fk are polynomials on X. Let
be the ideal generated by fi. It is well-known that there is a number e(I) (the Noether exponent) such that √Ie(I)⊂I. We give a sharp estimate of e(I) in terms of n, deg X
and deg fi. We also give similar estimates in the projective case. Finally we obtain a result from the elimination theory: if
is a system of polynomials with a finite number of common zeros, then we have the following optimal elimination:
where
. Dedicated to Professor Arkadiusz PłoskiMathematics Subject Classification (1991) 14D06, 14Q20 相似文献
16.
Adam Bobrowski 《Journal of Evolution Equations》2007,7(3):555-565
Let
be a locally compact Hausdorff space. Let A and B be two generators of Feller semigroups in
with related Feller processes {X
A
(t), t ≥ 0} and {X
B
(t), t ≥ 0} and let α and β be two non-negative continuous functions on
with α + β = 1. Assume that the closure C of C
0 = αA + βB with
generates a Feller semigroup {T
C
(t), t ≥ 0} in
. It is natural to think of a related Feller process {X
C
(t), t ≥ 0} as that evolving according to the following heuristic rules. Conditional on being at a point
, with probability α(p) the process behaves like {X
A
(t), t ≥ 0} and with probability β(p) it behaves like {X
B
(t), t ≥ 0}. We provide an approximation of {T
C
(t), t ≥ 0} via a sequence of semigroups acting in
that supports this interpretation. This work is motivated by the recent model of stochastic gene expression due to Lipniacki
et al. [17]. 相似文献
17.
Sergio Albeverio Alexander K. Motovilov Andrei A. Shkalikov 《Integral Equations and Operator Theory》2009,64(4):455-486
Let A be a self-adjoint operator on a Hilbert space . Assume that the spectrum of A consists of two disjoint components σ0 and σ1. Let V be a bounded operator on , off-diagonal and J-self-adjoint with respect to the orthogonal decomposition where and are the spectral subspaces of A associated with the spectral sets σ0 and σ1, respectively. We find (optimal) conditions on V guaranteeing that the perturbed operator L = A + V is similar to a self-adjoint operator. Moreover, we prove a number of (sharp) norm bounds on the variation of the spectral
subspaces of A under the perturbation V. Some of the results obtained are reformulated in terms of the Krein space theory. As an example, the quantum harmonic oscillator
under a -symmetric perturbation is discussed.
This work was supported by the Deutsche Forschungsgemeinschaft (DFG), the Heisenberg-Landau Program, and the Russian Foundation
for Basic Research. 相似文献
18.
We show that the algebra of functions on the scheme of monic linear second-order ordinary differential operators with prescribed
n + 1 regular singular points, prescribed exponents at the singular points, and having the kernel consisting of polynomials only, is isomorphic to the Bethe algebra of the Gaudin
model acting on the vector space Sing of singular vectors of weight Λ(∞) in the tensor product of finite-dimensional polynomial -modules with highest weights .
相似文献
19.
Abstract Consider an interstellar cloud that occupies the region
, bounded by the known surface
, and assume that the scattering cross section σs and the total cross section σ are also known. Then, we prove that it is possible to identify the source q=q(x,t) that produces UV-photons inside the cloud, provided that the UV-photon distribution function arriving at a location
, far from the cloud, is measured at times
,
, ...,
.
Keywords: Photon transport, Semigroups and linear evolution equations, Inverse problems
Mathematics Subject Classification (2000): 82A25, 82C70, 34K29, 65M32 相似文献
20.
Iterated Brownian Motion in Parabola-Shaped Domains 总被引:1,自引:0,他引:1
Erkan Nane 《Potential Analysis》2006,24(2):105-123
Iterated Brownian motion Zt serves as a physical model for diffusions in a crack. If τD(Z) is the first exit time of this processes from a domain D⊂ℝn, started at z∈D, then Pz[τD(Z)>t] is the distribution of the lifetime of the process in D. In this paper we determine the large time asymptotics of
which gives exponential integrability of
for parabola-shaped domains of the form Pα={(x,Y)∈ℝ×ℝn−1:x>0, |Y|<Axα}, for 0<α<1, A>0. We also obtain similar results for twisted domains in ℝ2 as defined in DeBlassie and Smits: Brownian motion in twisted domains, Preprint, 2004. In particular, for a planar iterated
Brownian motion in a parabola
we find that for z∈℘
Mathematics Subject Classifications (2000) 60J65, 60K99.
Erkan Nane: Supported in part by NSF Grant # 9700585-DMS. 相似文献