1,057 research outputs found
Generalized Projective Representations for sl(n+1)
It is well known that -dimensional projective group gives rise to a
non-homogenous representation of the Lie algebra on the polynomial
functions of the projective space. Using Shen's mixed product for Witt algebras
(also known as Larsson functor), we generalize the above representation of
to a non-homogenous representation on the tensor space of any
finite-dimensional irreducible -module with the polynomial space.
Moreover, the structure of such a representation is completely determined by
employing projection operator techniques and well-known Kostant's
characteristic identities for certain matrices with entries in the universal
enveloping algebra. In particular, we obtain a new one parameter family of
infinite-dimensional irreducible -modules, which are in general not
highest-weight type, for any given finite-dimensional irreducible
-module. The results could also be used to study the quantum field
theory with the projective group as the symmetry.Comment: 24page
Stress-induced permeability evolution in coal: Laboratory testing and numerical simulations
Mining operations produce a multiscale network of fractures in the coal seams. Permeability evolution in rocks is important for coal bed methane (CBM) and shale gas exploitation as well as for greenhouse gas storage. Therefore, this work presents laboratory tests and a coupled model using PFC3D and FLAC3D to simulate the stress induced permeability evolution in coal samples. Basic mechanical properties are determined via lab testing. The spatial distributions of different components inside the reconstructed samples produce a significant heterogeneity based on CT technique. A newly developed experimental system is employed to perform 3-dimensional loading and to measure the flow rate simultaneously. The evolution process is described by 5 distinct phases in terms of permeability and deformation. Triaxial tests are simulated with PFC3D using a novel flexible wall boundary method. Gas seepage simulations are performed with FLAC3D. Relations between hydraulic properties and fracture data are established. Permeability and volumetric strain show good nonlinear exponential relation after a newly introduced expansion point. Piecewise relations fit the whole process, the expansion point can be treated as critical point. The structural characteristics of the samples influence this relation before and after the expansion point significantly
Descriptions of strongly multiplicity free representations for simple Lie algebras
Let be a simple Lie algebra over the complex numbers
. Let be the center of the universal enveloping
algebra . Denote by the finite-dimensional simple
-module with highest weight . Lehrer and Zhang defined
the notion of strongly multiplicity free representations for simple Lie
algebras motivited by studying the structure of the endomorphism algebras in terms of the quotients of Kohno's
infinitesimal braid algebra. Kostant introduced the -invariant
endomorphism algebras and In this paper, we give some other
criterion for a multiplicity free representation to be a strongly multiplicity
free representation for simple Lie algebras by classifing the pairs
, which are multiplicity free irreducible modules
and for such pairs, and are generated by
generalizations of the quadratic Casimimir elements of
The effect of substrate temperature on cadmium telluride films in high temperature vapor deposition process
Physical vapor high-temperature deposition of CdTe thin films is one of the
main methods for preparing high-efficiency CdTe solar cells, but
high-temperature deposition also has an impact on the internal structure of the
film. The difference in thermal expansion coefficients between the substrate
and CdTe leads to the generation of internal stress in the CdTe thin film
during the cooling process. In this work, we prepared thin films with different
substrate temperatures using a homemade GVD device, and observed by SEM that
the crystallization quality of the film gradually improved with the increase of
substrate temperature, but accompanied by the shift of XRD peak position. We
calculated the internal stress situation of the film by the shift amount, and
the possible causes of stress generation were speculated by the results of TEM
and SAED to be the combined effects of the different thermal expansion
coefficients between the substrate and the film and the stacking fault defects
inside the film
Strongly Commuting Ring and The Prounet-Tarry-Escott Problem
In 1935, Wright conjectured that ideal solutions to the PTE problem in
Diophantine number theory should exist. In this paper, we prove Wright's
conjecture holds true based on the the representation theory of the minuscule
strongly commuting ring introduced by Kostant in 1975 and the complex
coefficient cohomology ring structures of the Grassmannian variey
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