1,386 research outputs found
On multigraded generalizations of Kirillov-Reshetikhin modules
We study the category of Z^l-graded modules with finite-dimensional graded
pieces for certain Z+^l-graded Lie algebras. We also consider certain Serre
subcategories with finitely many isomorphism classes of simple objects. We
construct projective resolutions for the simple modules in these categories and
compute the Ext groups between simple modules. We show that the projective
covers of the simple modules in these Serre subcategories can be regarded as
multigraded generalizations of Kirillov-Reshetikhin modules and give a
recursive formula for computing their graded characters
Equivariant map superalgebras
Suppose a group acts on a scheme and a Lie superalgebra
. The corresponding equivariant map superalgebra is the Lie
superalgebra of equivariant regular maps from to . We
classify the irreducible finite dimensional modules for these superalgebras
under the assumptions that the coordinate ring of is finitely generated,
is finite abelian and acts freely on the rational points of , and
is a basic classical Lie superalgebra (or ,
, if is trivial). We show that they are all (tensor products
of) generalized evaluation modules and are parameterized by a certain set of
equivariant finitely supported maps defined on . Furthermore, in the case
that the even part of is semisimple, we show that all such
modules are in fact (tensor products of) evaluation modules. On the other hand,
if the even part of is not semisimple (more generally, if
is of type I), we introduce a natural generalization of Kac
modules and show that all irreducible finite dimensional modules are quotients
of these. As a special case, our results give the first classification of the
irreducible finite dimensional modules for twisted loop superalgebras.Comment: 27 pages. v2: Section numbering changed to match published version.
Other minor corrections. v3: Minor corrections (see change log at end of
introduction
Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
Let Uq(ghat) be the quantum affine algebra associated to a simply-laced
simple Lie algebra g. We examine the relationship between Dorey's rule, which
is a geometrical statement about Coxeter orbits of g-weights, and the structure
of q-characters of fundamental representations V_{i,a} of Uq(ghat). In
particular, we prove, without recourse to the ADE classification, that the rule
provides a necessary and sufficient condition for the monomial 1 to appear in
the q-character of a three-fold tensor product V_{i,a} x V_{j,b} x V_{k,c}.Comment: 30 pages, latex; v2, to appear in Communications in Mathematical
Physic
Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)]
There being no precise definition of the quantum integrability, the
separability of variables can serve as its practical substitute. For any
quantum integrable model generated by the Yangian Y[sl(3)] the canonical
coordinates and the conjugated operators are constructed which satisfy the
``quantum characteristic equation'' (quantum counterpart of the spectral
algebraic curve for the L operator). The coordinates constructed provide a
local separation of variables. The conditions are enlisted which are necessary
for the global separation of variables to take place.Comment: 15 page
R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
We review some of the strategies that can be implemented to infer an
-matrix from the knowledge of its Hamiltonian. We apply them to the
classification achieved in arXiv:1306.6303, on three state -invariant
Hamiltonians solvable by CBA, focusing on models for which the -matrix is
not trivial.
For the 19-vertex solutions, we recover the -matrices of the well-known
Zamolodchikov--Fateev and Izergin--Korepin models. We point out that the
generalized Bariev Hamiltonian is related to both main and special branches
studied by Martins in arXiv:1303.4010, that we prove to generate the same
Hamiltonian. The 19-vertex SpR model still resists to the analysis, although we
are able to state some no-go theorems on its -matrix.
For 17-vertex Hamiltonians, we produce a new -matrix.Comment: 22 page
Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)
We investigate a one-parameter family of quantum Harish-Chandra modules of
U_q sl(2n). This family is an analog of the holomorphic discrete series of
representations of the group SU(n,n) for the quantum group U_q su(n, n). We
introduce a q-analog of "the wave" operator (a determinant-type differential
operator) and prove certain covariance property of its powers. This result is
applied to the study of some quotients of the above-mentioned quantum
Harish-Chandra modules. We also prove an analog of a known result by J.Faraut
and A.Koranyi on the expansion of reproducing kernels which determines the
analytic continuation of the holomorphic discrete series.Comment: 26 page
Poisson Realization and Quantization of the Geroch Group
The conserved nonlocal charges generating the Geroch group with respect to
the canonical Poisson structure of the Ernst equation are found. They are shown
to build a quadratic Poisson algebra, which suggests to identify the quantum
Geroch algebra with Yangian structures.Comment: 8 pages, LaTeX2
Noncommutative fields and actions of twisted Poincare algebra
Within the context of the twisted Poincar\'e algebra, there exists no
noncommutative analogue of the Minkowski space interpreted as the homogeneous
space of the Poincar\'e group quotiented by the Lorentz group. The usual
definition of commutative classical fields as sections of associated vector
bundles on the homogeneous space does not generalise to the noncommutative
setting, and the twisted Poincar\'e algebra does not act on noncommutative
fields in a canonical way. We make a tentative proposal for the definition of
noncommutative classical fields of any spin over the Moyal space, which has the
desired representation theoretical properties. We also suggest a way to search
for noncommutative Minkowski spaces suitable for studying noncommutative field
theory with deformed Poincar\'e symmetries.Comment: 20 page
Multi-parameter deformed and nonstandard Yangian symmetry in integrable variants of Haldane-Shastry spin chain
By using `anyon like' representations of permutation algebra, which pick up
nontrivial phase factors while interchanging the spins of two lattice sites, we
construct some integrable variants of Haldane-Shastry (HS) spin chain. Lax
equations for these spin chains allow us to find out the related conserved
quantities. However, it turns out that such spin chains also possess a few
additional conserved quantities which are apparently not derivable from the Lax
equations. Identifying these additional conserved quantities, and the usual
ones related to Lax equations, with different modes of a monodromy matrix, it
is shown that the above mentioned HS like spin chains exhibit multi-parameter
deformed and `nonstandard' variants of Yangian symmetry.Comment: 18 pages, latex, no figure
The Effect of Propofol on the Canine Sphincter of Oddi
To assess the effect of propofol on the canine sphincter of Oddi (SO), sphincter of Oddi manometry (SOM)
was performed in fasting dogs which had undergone cholecystectomy and placement of modified Thomas
duodenal cannulae. Using two water-perfused, single-lumen manometric catheters, SO and duodenal
pressures were measured simultaneously. Baseline SO activity was recorded for at least one complete
interdigestive cycle followed by bolus injections of propofol (Diprivan ®) (N = 31) from 0.1 to 4.0 mg/kg
during Phase I of the Migrating Motor Complex (MMC)
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