4,530 research outputs found
Free field realizations of the Date-Jimbo-Kashiwara-Miwa algebra
We use the description of the universal central extension of the DJKM algebra
where
given in earlier work to construct realizations of the DJKM algebra in terms of
sums of partial differential operators.Comment: arXiv admin note: substantial text overlap with arXiv:1303.697
Langlands duality for representations of quantum groups
We establish a correspondence (or duality) between the characters and the
crystal bases of finite-dimensional representations of quantum groups
associated to Langlands dual semi-simple Lie algebras. This duality may also be
stated purely in terms of semi-simple Lie algebras. To explain this duality, we
introduce an "interpolating quantum group" depending on two parameters which
interpolates between a quantum group and its Langlands dual. We construct
examples of its representations, depending on two parameters, which interpolate
between representations of two Langlands dual quantum groups.Comment: 37 pages. References added. Accepted for publication in Mathematische
Annale
Gaudin models with irregular singularities
We introduce a class of quantum integrable systems generalizing the Gaudin
model. The corresponding algebras of quantum Hamiltonians are obtained as
quotients of the center of the enveloping algebra of an affine Kac-Moody
algebra at the critical level, extending the construction of higher Gaudin
Hamiltonians from hep-th/9402022 to the case of non-highest weight
representations of affine algebras. We show that these algebras are isomorphic
to algebras of functions on the spaces of opers on P^1 with regular as well as
irregular singularities at finitely many points. We construct eigenvectors of
these Hamiltonians, using Wakimoto modules of critical level, and show that
their spectra on finite-dimensional representations are given by opers with
trivial monodromy. We also comment on the connection between the generalized
Gaudin models and the geometric Langlands correspondence with ramification.Comment: Latex, 72 pages. Final version to appear in Advances in Mathematic
Constructing quantum vertex algebras
This is a sequel to \cite{li-qva}. In this paper, we focus on the
construction of quantum vertex algebras over \C, whose notion was formulated
in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator
algebra (over \C[[h]]) as one of the main motivations. As one of the main
steps in constructing quantum vertex algebras, we prove that every
countable-dimensional nonlocal (namely noncommutative) vertex algebra over
\C, which either is irreducible or has a basis of PBW type, is nondegenerate
in the sense of Etingof and Kazhdan. Using this result, we establish the
nondegeneracy of better known vertex operator algebras and some nonlocal vertex
algebras. We then construct a family of quantum vertex algebras closely related
to Zamolodchikov-Faddeev algebras.Comment: 37 page
Boundary Friction on Molecular Lubricants: Rolling Mode?
A theoretical model is proposed for low temperature friction between two
smooth rigid solid surfaces separated by lubricant molecules, admitting their
deformations and rotations. Appearance of different modes of energy dissipation
(by ''rocking'' or ''rolling'' of lubricants) at slow relative displacement of
the surfaces is shown to be accompanied by the stick-and-slip features and
reveals a non-monotonic (mean) friction force {\it vs} external loadComment: revtex4, 4 pages, 5 figure
Extended T-systems
We use the theory of q-characters to establish a number of short exact
sequences in the category of finite-dimensional representations of the quantum
affine groups of types A and B. That allows us to introduce a set of 3-term
recurrence relations which contains the celebrated T-system as a special case.Comment: 36 pages, latex; v2: version to appear in Selecta Mathematic
Devil's staircase of incompressible electron states in a nanotube
It is shown that a periodic potential applied to a nanotube can lock
electrons into incompressible states. Depending on whether electrons are weakly
or tightly bound to the potential, excitation gaps open up either due to the
Bragg diffraction enhanced by the Tomonaga - Luttinger correlations, or via
pinning of the Wigner crystal. Incompressible states can be detected in a
Thouless pump setup, in which a slowly moving periodic potential induces
quantized current, with a possibility to pump on average a fraction of an
electron per cycle as a result of interactions.Comment: 4 pages, 1 figure, published versio
The Integrals of Motion for the Deformed W-Algebra II: Proof of the commutation relations
We explicitly construct two classes of infinitly many commutative operators
in terms of the deformed W-algebra , and give proofs of the
commutation relations of these operators. We call one of them local integrals
of motion and the other nonlocal one, since they can be regarded as elliptic
deformation of local and nonlocal integrals of motion for the algebra.Comment: Dedicated to Professor Tetsuji Miwa on the occasion on the 60th
birthda
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