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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.
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
3.
The product of two real spectral triples
and
, the first of which is necessarily even, was defined by A.Connes as
given by
and, in the even-even case, by
. Generically it is assumed that the real structure
obeys the relations
,
,
, where the
-sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes'
>-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this
-sign table. In this Letter, we propose an alternative definition of the product real structure such that the
-sign table is also satisfied by the product. 相似文献
4.
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
5.
Lu has shown that any dynamical r-matrix for the pair (
,
) naturally induces a Poisson homogeneous structure on G/U. She also proved that if
is complex simple,
is its Cartan subalgebra and r is quasitriangular, then this correspondence is in fact one-to-one. In this Letter we find some general conditions under which the Lu correspondence is one-to-one. Then we apply this result to describe all triangular Poisson homogeneous structures on G/U for a simple complex group G and its reductive subgroup U containing a Cartan subgroup. 相似文献
6.
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
7.
In this Letter, we consider Kontsevich's wheel operators for linear Poisson structures, i.e. on the dual of Lie algebras
. We prove that these operators vanish on each invariant polynomial function on
*. This gives a characterization of the Kontsevich star products which are deformations relative to the algebra of invariant functions. 相似文献
8.
Let
be von Neumann algebras acting on a Hilbert space
and let
be a common cyclic and separating vector. We say that
have the modular intersection property with respect to
if(1)
-half-sided modular inclusions,(2)
(If (1) holds the strong limit exists.) We show that under these conditions the modular groups of
and
generate a 2-dim. Lie group.This observation is the basis for obtaining group representations of Sl(2,
)/Z
2 generated by modular groups. 相似文献
9.
The universal R-matrix for a class of esoteric (nonstandard) quantum groups
q(gl(2N+1)) is constructed as a twisting of the universal R-matrix
S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle
is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's
(N)
q (gl(2N+1))), providing the factorization property of
. As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo. 相似文献
10.
We propose a q-deformation of the
-invariant Schrödinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but also to calculate the expectation values of some physically-relevant operators. Here we consider the case of the isotropic harmonic oscillator and of the quadrupole operator governing its interaction with an external field. We obtain the spectrum and wave functions both for
and generic
, and study the effects of the q-value range and of the arbitrariness in the
Casimir operator choice. We then show that the quadrupole operator in l=0 states provides a good measure of the deformation influence on the wave functions and on the Hilbert space spanned by them. 相似文献
11.
J. Donin 《Czechoslovak Journal of Physics》1997,47(11):1115-1122
For
we construct a two parametric
-invariant family of algebras,
, that is a quantization of the function algebra
on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric
-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on
. 相似文献
12.
We show that the affine quantum group
is isomorphic to a bicross-product central extension
of the quantum loop group
by a quantum cocycle
in R-matrix form. 相似文献
13.
We consider the Dirichlet Laplacian for astrip in
with one straight boundary and a width
, where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase,
, the operator has nobound statesfor small
.On the otherhand, a weakly bound state existsprovided
. In thatcase, there are positive c
1,c
2 suchthat the corresponding eigenvalue satisfies
for all
sufficiently small. 相似文献
14.
Let
be a finite-dimensional complex simple Lie algebra and Uq(
) the associated quantum group (q is a nonzero complex number which we assume is transcendental). IfV is a finitedimensional irreducible representation of Uq(
), an affinization ofV is an irreducible representationVV of the quantum affine algebra Uq(
) which containsV with multiplicity one and is such that all other irreducible Uq(
)-components ofV have highest weight strictly smaller than the highest weight ofV. There is a natural partial order on the set of Uq(
) classes of affinizations, and we look for the minimal one(s). In earlier papers, we showed that (i) if
is of typeA, B, C, F orG, the minimal affinization is unique up to Uq(
)-isomorphism; (ii) if
is of typeD orE and is not orthogonal to the triple node of the Dynkin diagram of
, there are either one or three minimal affinizations (depending on ). In this paper, we show, in contrast to the regular case, that if Uq(
) is of typeD
4 and is orthogonal to the triple node, the number of minimal affinizations has no upper bound independent of .As a by-product of our methods, we disprove a conjecture according to which, if
is of typeA
n,every affinization is isomorphic to a tensor product of representations of Uq(
) which are irreducible under Uq(
) (in an earlier paper, we proved this conjecture whenn=1).Both authors were partially supported by the NSF, DMS-9207701. 相似文献
15.
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
16.
17.
Let X be a connected Riemann surface equipped with a projective structure
. Let E be a holomorphic symplectic vector bundle over X equipped with a flat connection. There is a holomorphic symplectic structure on the total space of the pullback of E to the space of all nonzero holomorphic cotangent vectors on X. Using
, this symplectic form is quantized. A moduli space of Higgs bundles on a compact Riemann surface has a natural holomorphic symplectic structure. Using
, a quantization of this symplectic form over a Zariski open subset of the moduli space of Higgs bundles is constructed. 相似文献
18.
We derive explicit formulas for the multipoint series of
in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of
. We also obtain explicit formulas for the Hodge integrals
, in the cases i=0 and 1. 相似文献
19.
The zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite-dimensional state space. A generalized BRS operator A such that
being the height of the current algebra representation) acts in
-dimensional indefinite metric space
of quantum group invariant vectors. The generalized cohomologies Ker
are 1-dimensional. Their direct sum spans the physical subquotient of
. 相似文献
20.
We present several formulae for Selberg-type integrals associated with the Lie algebra
. 相似文献