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Full-Text Articles in Physical Sciences and Mathematics
Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys
Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys
Mathematics and Statistics Department Faculty Publication Series
In this note we study simple modules for a reduced enveloping algebra Ux (g) in the critical case when X E 2 g^x is “nilpotent”. Some dimension formulas computed by Jantzen suggest modified versions of Weyl’s dimension formula, based on certain reflecting hyperplanes for the affine Weyl group which might be associated to Kazhdan–Lusztig cells.
Structure Of The Malvenuto-Reutenauer Hopf Algebra Of Permutations (Extended Abstract), Marcelo Aguiar, Frank Sottile
Structure Of The Malvenuto-Reutenauer Hopf Algebra Of Permutations (Extended Abstract), Marcelo Aguiar, Frank Sottile
Mathematics and Statistics Department Faculty Publication Series
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive elements and its coradical filtration and show that it decomposes as a crossed product over the Hopf algebra of quasi-symmetric functions. We also describe the structure constants of the multiplication as a certain number of facets of the permutahedron. Our results reveal a close relationship between the structure of this Hopf algebra and the weak order on the symmetric groups.
Scattering Of A Solitary Pulse On A Local Defect Or Breather, Panayotis G. Kevrekidis, Boris A. Malomed, H. E. Nistazakis, Dimitri J. Frantzeskakis, A. Saxena, A. R. Bishop
Scattering Of A Solitary Pulse On A Local Defect Or Breather, Panayotis G. Kevrekidis, Boris A. Malomed, H. E. Nistazakis, Dimitri J. Frantzeskakis, A. Saxena, A. R. Bishop
Mathematics and Statistics Department Faculty Publication Series
A model is introduced to describe guided propagation of a linear or nonlinear pulse which encounters a localized nonlinear defect, that may be either static or breather-like one. The model with the static defect directly applies to an optical pulse in a long fiber link with an inserted additional section of a nonlinear fiber. A local breather which gives rise to the nonlinear defect affecting the propagation of a narrow optical pulse is possible in a molecular chain. In the case when the host waveguide is linear, the pulse has a Gaussian shape. In that case, an immediate result of …