共查询到20条相似文献,搜索用时 718 毫秒
1.
Lucy Gow 《Czechoslovak Journal of Physics》2005,55(11):1415-1420
Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y
of the general linear Lie algebra
. In this article, we extend some of their ideas to consider the Yangian Y
of the Lie superalgebra
. In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
2.
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
3.
This Letter concerns an extension of the quantum spinor construction of
. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, and construct quantum spinor representations of
. 相似文献
4.
Ruedi Suter 《Communications in Mathematical Physics》1994,163(2):359-393
The restricted quantum universal enveloping algebra
decomposes in a canonical way into a direct sum of indecomposable left (or right) ideals. They are useful for determining the direct summands which occur in the tensor product of two simple
. The indecomposable finite-dimensional
are classified and located in the Auslander-Reiten quiver. 相似文献
5.
The Lie algebra
is “deformed” using twisted derivations satisfying a twisted Leibniz rule. Some particular algebras appearing in this deformation
scheme are discussed.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.
Supported by the Liegrits network
Supported by the Crafoord foundation 相似文献
6.
Pavel Šťovíček 《Czechoslovak Journal of Physics》2000,50(11):1353-1358
We discuss a modification ofU
q
and a class of its irreducible representations whenq is a root of unity.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. 相似文献
7.
We establish an explicit isomorphism between two realizations of the quantum affine algebra
given previously by Drinfeld and Reshetikhin-Semenov-Tian-Shansky. Our result can be considered as an affine version of the isomorphism between the Drinfield/Jimbo and the Faddeev-Reshetikhin-Takhtajan constructions of the quantum algebra
. 相似文献
8.
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
9.
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
10.
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.
Theq=0 combinatorics for
is studied in connection with solvable lattice models. Crystal bases of highest weight representations of
are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors atq=0. It is shown that the crystal graphs for finite tensor products ofl-th symmetric tensor representations of
approximate the crystal graphs of levell representations of
. The identification is made between restricted paths for the RSOS models and highest weight vectors in the crystal graphs of tensor modules for
.Partially supported by NSF grant MDA904-90-H-4039 相似文献
13.
14.
G. Lévai 《Czechoslovak Journal of Physics》2006,56(9):953-966
The Scarf I and Scarf II potentials are discussed within a common mathematical framework, which is then specified to handle
the two potentials separately both in the conventional Hermitian and in the
-symmetric setting. The physically admissible solutions are identified in each case together with the corresponding energy
eigenvalues. Several main differences between the
-symmetric Scarf I and II potentials are pointed out. These include the presence and absence of the quasi-parity quantum number,
the sign of the pseudo-norm, the mechanism of the spontaneous breakdown of
symmetry and the non-
orthogonality of otherwise admissible solutions in the Scarf I potential. Similarities and differences with respect to the
corresponding Hermitian systems are also pointed out. 相似文献
15.
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
16.
Ch. Ohn 《Letters in Mathematical Physics》1992,25(2):85-88
We obtain Zakrzewski's deformation of Fun SL(2) through the construction of a *-product on SL(2). We then give the deformation of
dual to this, as well as a Poincaré basis for both algebras.Aspirant au Fonds National belge de la Recherche Scientifique. Partially supported by EEC contract SC1-0105-C. 相似文献
17.
Recently, A. A. Kirillov introduced an important notion of classical and quantum family algebras. Here the criterion of commutativity is given. The quantum eigenvalues of
are computed. 相似文献
18.
Miloslav Znojil 《Czechoslovak Journal of Physics》2006,56(9):977-984
A review of a few recent developments in our analysis and applications of the coupled-channel version of the formalism of
-symmetric quantum mechanics is given. 相似文献
19.
The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy
(where
0$$
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and
0$$
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are two constants). In particular, the perpendicular incidence of an electron with a given value
of the wave vector
is considered. The electron is forward-scattered into the region behind the barrier (region 2:
0$$
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), i. e. the wave function
is composed of plane waves with all wave vectors
such that
and
\left. 0 \right)} $$
" align="middle" border="0">
) (where
). Therefore, if
0$$
" align="middle" border="0">
, the wave function of the electron is represented as
, where
. An approximate formula is derived for the amplitude
. The authors pay a special attention to the flow density
and calculate this function in two cases: 1. for the plane
and 2. for high values of
is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier. 相似文献
20.
We define and calculate the fusion algebra of a WZW model at a rational level using cohomological methods. As a byproduct, we obtain a cohomological characterization of admissible representations of
2. 相似文献