179 research outputs found
Yangians and Mickelsson Algebras I
We study the composition of the functor from the category of modules over the
Lie algebra gl_m to the category of modules over the degenerate affine Hecke
algebra of GL_N introduced by I. Cherednik, with the functor from the latter
category to the category of modules over the Yangian Y(gl_n) due to V.
Drinfeld. We propose a representation theoretic explanation of a link between
the intertwining operators on the tensor products of Y(gl_n)-modules, and the
`extremal cocycle' on the Weyl group of gl_m defined by D. Zhelobenko. We also
establish a connection between the composition of two functors, and the
`centralizer construction' of the Yangian Y(gl_n) discovered by G. Olshanski.Comment: publication details added. arXiv admin note: substantial text overlap
with arXiv:math/060627
Exact constants in Poincare type inequalities for functions with zero mean boundary traces
In the paper, we investigate Poincare type inequalities for the functions
having zero mean value on the whole boundary of a Lipschitz domain or on a
measurable part of the boundary. We derive exact and easily computable
constants for some basic domains (rectangles, cubes, and right triangles). In
the last section, we derive an a estimate of the difference between the exact
solutions of two boundary value problems. Constants in Poincare type
inequalities enter these estimates, which provide guaranteed a posteriori error
control.Comment: A gap in the proof of Theorem 3.2 is fixed; 19 pages, 3 figure
Scalar problems in junctions of rods and a plate. II. Self-adjoint extensions and simulation models
In this work we deal with a scalar spectral mixed boundary value problem in a
spacial junction of thin rods and a plate. Constructing asymptotics of the
eigenvalues, we employ two equipollent asymptotic models posed on the skeleton
of the junction, that is, a hybrid domain. We, first, use the technique of
self-adjoint extensions and, second, we impose algebraic conditions at the
junction points in order to compile a problem in a function space with detached
asymptotics. The latter problem is involved into a symmetric generalized Green
formula and, therefore, admits the variational formulation. In comparison with
a primordial asymptotic procedure, these two models provide much better
proximity of the spectra of the problems in the spacial junction and in its
skeleton. However, they exhibit the negative spectrum of finite multiplicity
and for these "parasitic" eigenvalues we derive asymptotic formulas to
demonstrate that they do not belong to the service area of the developed
asymptotic models.Comment: 31 pages, 2 figur
Twisted Yangians and Mickelsson Algebras II
We introduce a skew analogue of the composition of the Cherednik and Drinfeld
functors for twisted Yangians. Our definition is based on the skew Howe
duality, and originates from the centralizer construction of twisted Yangians
due to Olshanski. Using our functor, we establish a correspondence between
intertwining operators on the tensor products of certain modules over twisted
Yangians, and the extremal cocycle on the hyperoctahedral group.Comment: final versio
A criterion for the existence of the essential spectrum for beak-shaped elastic bodies
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