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1.
Given a simple, simply laced, complex Lie algebra
corresponding to the Lie group G, let
be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra
whose underlying graded commutative algebra is given by the cohomology, with respect to
, of the algebra of regular functions on G with values in
. We conjecture that
describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical
string. The conjecture is verified in the two explicitly known cases,
2 (the Virasoro string) and
3 (the
string). 相似文献
2.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
3.
We give an expression of theq-analogues of the multiplicities of weights in irreducible
in terms of the geometry of the crystal graph attached to corresponding
. As an application, we describe multivariate polynomial analogues of the multiplicities of the zero weight, refining Kostant's generalized exponents.Partially supported by PRC Math-Info and EEC grant No. ERBCHRXCT930400. 相似文献
4.
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group
in the following manner. There is a partition
into disjoint subsets and a bijection between
and the sectors
of the (p,q)-minimal model such that the fusion rules
correspond to
where
. 相似文献
5.
Let (M, g) be a pseudo-Riemannian manifold and
the space of densities of degree on M. Denote
the space of differential operators from
to
of order k and S
k
with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map
. This result generalizes that of Duval and Ovsienko. 相似文献
6.
A simplified construction of representations is presented for the quantized enveloping algebra
q (
), with
being a simple complex Lie algebra belonging to one of the four principal series A\ell, B\ell, C\ell or D\ell. The carrier representation space is the quantized algebra of polynomials in antiholomorphic coordinate functions on the big cell of a coadjoint orbit of K where K is the compact simple Lie group with the Lie algebra
– the compact form of
. 相似文献
7.
We prove a simple formula for the transverse Poisson structure to a coadjoint orbit (in the dual of a Lie algebra
) and use it in examples such as
and
. We also give a sufficient condition on the isotropy subalgebra of
so that the transverse Poisson structureto the coadjoint orbit of is linear. 相似文献
8.
J. De Cannière 《Communications in Mathematical Physics》1982,84(2):187-205
Let be a state on aC*-dynamical system
. For each of the following properties of : (1) is -K MS with respect to for some given , 0<+, (2) is either a KMS state or a ground state, necessary and sufficient conditions are given involving only the spectral subspaces of
associated with . The results provide a new insight in the concept of passivity, introduced by W. Pusz and S. L. Woronowicz.Aangesteld navorser N.F.W.O., Belgium, on leave from Katholieke Universiteit Leuven. Research partially supported by N.A.T.O. 相似文献
9.
Karl Kraus 《Communications in Mathematical Physics》1967,7(2):99-111
Concrete C*-algebras, interpreted physically as algebras of observables, are defined for quantum mechanics and local quantum field theory.Aquantum mechanical system is characterized formally by a continuous unitary representation up to a factorU
g
of a symmetry group
in Hilbert space and a von Neumann algebra on invariant with respect toU
g
. The set
of all operatorsX such thatU
g
X U
g
–1
, as a function ofg
, is continuous with respect to the uniform operator topology, is aC*-algebra called thealgebra of observables. The algebra is shown to be the weak (or strong) closure of
.Infield theory, a unitary representation up to a factorU(a, ) of the proper inhomogeneous Lorentz group
and local von Neumann algebras C for finite open space-time regionsC are assumed, with the usual transformation properties of
underU(a, ). The collection of allXC giving uniformly continuous functionsU (a, )X U
–1 (a, ) on
is then a localC*-algebra
, called thealgebra of local observables. The algebra
is again weakly (or strongly) dense in
c
. The norm-closed union
of the
for allC is calledalgebra of quasilocal observables (or quasilocal algebra).In either case, the group
is represented by automorphisms V
g
resp. V(a, ) — with V
g
X=U
g
X U
g
–1
— of theC*-algebra
, and this is astrongly continuous representation of
on the Banach space
. Conditions for V (a, ) can then be formulated which correspond to the usualspectrum condition forU (a, ) in field theory.Work supported in part by the Deutsche Forschungsgemeinschaft. 相似文献
10.
We present several formulae for Selberg-type integrals associated with the Lie algebra
. 相似文献
11.
Given n2, we put r=min
. Let be a compact, C
r
-smooth surface in n which contains the origin. Let further
be a family of measurable subsets of such that
as
. We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator
in L
2(
n
), where is a positive constant, as
. An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve. 相似文献
12.
We consider Kontsevich star products on the duals of Lie algebras. Such a star product is relative if, for any Lie algebra, its restriction to invariant polynomial functions is the usual pointwise product. Let
be a fixed Lie algebra. We shall say that a Kontsevich star product is
-relative if, on
*, its restriction to invariant polynomial functions is the usual pointwise product. We prove that, if
is a semi-simple Lie algebra, the only strict Kontsevich
-relative star products are the relative (for every Lie algebras) Kontsevich star products. 相似文献
13.
A quantum analogue of the dual pair
is introduced in terms of the oscillator representation of U
q
. Its commutant and the associated identity of Capelli type are discussed. 相似文献
14.
Let (, d) be a first-order differential *-calculus on a *-algebra
. We say that a pair (, F) of a *-representation of
on a dense domain
of a Hilbert space and a symmetric operator F on
gives a commutator representation of if there exists a linear mapping : L(
) such that (adb) = (a)i[F, (b) ], a, b
. Among others, it is shown that each left-covariant *-calculus of a compact quantum group Hopf *-algebra
has a faithful commutator representation. For a class of bicovariant *-calculi on
, there is a commutator representation such that F is the image of a central element of the quantum tangent space. If
is the Hopf *-algebra of the compact form of one of the quantum groups SL
q
(n+1), O
q
(n), Sp
q
(2n) with real trancendental q, then this commutator representation is faithful. 相似文献
15.
BRST resolution is studied for the principally graded Wakimoto module of
recently found in math.QA/0005203. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group. 相似文献
16.
Wang Zheng Dong 《Letters in Mathematical Physics》1996,38(4):377-388
By considering the cohomology of the loop algebraL
, a representation ofL
is constructed. the construction is based on a derivation ofL
and a two-dimensional closed cochain ofl
with coefficients in real numbersR
1. In the case of =0, the differential of the energy representation of the corresponding loop groupLG is derived.This work was supported in part by the National Natural Science Foundation of China. 相似文献
17.
The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra
(m/n ) were described by Serganova, leading to her solution of the character problem for
(m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed. 相似文献
18.
We study analogues of the Yangian of the Lie algebra
for the other classical Lie algebras
and
. We call them twisted Yangians. They are coideal subalgebras in the Yangian of
and admit homomorphisms onto the universal enveloping algebras U(
) and U(
) respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in U(
) and U(
) of these subalgebras are also maximal commutative. 相似文献
19.
We define a quantum-algebra associated to
as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary-algebra of
, or theq-deformed classical-algebra algebra of
. We construct free field realizations of the quantum-algebra and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in.The research of the second author was partially supported by NSF grant DMS-9501414. 相似文献
20.
S. Hein 《Letters in Mathematical Physics》1985,10(4):263-268
There is widespread prejudice that the existence of Bose-condensed equilibrium states of infinite ideal boson gas requires chemical potential to be strictly zero. This is not true, in general. Using standard techniques of algebraic QFT only, we show that there exists e
ith
invariant extensions T of Schwartz's space D(3) and Bose-condensed KMS states on the CCR algebra
(T) for every chemical potential 0 (h=––, the one-particle Hamiltonian). The corresponding condensation fields are, in general, of rapid growth at infinity, with suggested physical implications. 相似文献