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Physical Sciences and Mathematics Commons™
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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
A Polytope Combinatorics For Semisimple Groups, Jared E. Anderson
A Polytope Combinatorics For Semisimple Groups, Jared E. Anderson
Mathematics and Statistics Department Faculty Publication Series
Mirkovi and Vilonen discovered a canonical basis of algebraic cycles for the intersection homology of (the closures of the strata of) the loop Grassmannian. The moment map images of these varieties are a collection of polytopes, and they may be used to compute weight multiplicities and tensor product multiplicities for representations of a semisimple group. The polytopes are explicitly described for a few low rank groups.
Quaternionic Holomorphic Geometry: Plucker Formula, Dirac Eigenvalue Estimates And Energy Estimates Of Harmonic 2-Tori, D Ferus, K Leschke, F Pedit, U Pinkall
Quaternionic Holomorphic Geometry: Plucker Formula, Dirac Eigenvalue Estimates And Energy Estimates Of Harmonic 2-Tori, D Ferus, K Leschke, F Pedit, U Pinkall
Mathematics and Statistics Department Faculty Publication Series
No abstract provided.
Geometric Representation Theory Of Restricted Lie Algebras, I Mirkovic, D Rumynin
Geometric Representation Theory Of Restricted Lie Algebras, I Mirkovic, D Rumynin
Mathematics and Statistics Department Faculty Publication Series
We modify the Hochschild -map to construct central extensions of a restricted Lie algebra. Such central extension gives rise to a goup scheme that leads to a geometric construction of unrestricted representations. For a classical semisimple Lie algebra, we construct equivariant line bundles whose global sections afford representations with a nilpotentp-character.
Statistical Equilibrium Measures In Micromagnetics, Ma Katsoulakis, P Plechac
Statistical Equilibrium Measures In Micromagnetics, Ma Katsoulakis, P Plechac
Mathematics and Statistics Department Faculty Publication Series
We derive an equilibrium statistical theory for the macroscopic description of a ferromagnetic material at positive finite temperatures. Our formulation describes the most-probable equilibrium macrostates that yield a coherent deterministic large-scale picture varying at the size of the domain, as well as it captures the effect of random spin fluctuations caused by the thermal noise. We discuss connections of the proposed formulation to the Landau-Lifschitz theory and to the studies of domain formation based on Monte Carlo lattice simulations.
Bilinear Operators With Non-Smooth Symbol, I, John E. Gilbert, Andrea R. Nahmod
Bilinear Operators With Non-Smooth Symbol, I, John E. Gilbert, Andrea R. Nahmod
Mathematics and Statistics Department Faculty Publication Series
This paper proves the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilbert transform of Lacey-Thiele, where the multiplier is not smooth. Using a Whitney decomposition in the Fourier plane a general bilinear operator is represented as infinite discrete sums of time-frequency paraproducts obtained by associating wave-packets with tiles …
Complementary Algorithms For Tableaux, Tom Roby, Frank Sottile, Jeff Stroomer, Julian West
Complementary Algorithms For Tableaux, Tom Roby, Frank Sottile, Jeff Stroomer, Julian West
Mathematics and Statistics Department Faculty Publication Series
We study four operations defined on pairs of tableaux. Algorithms for the first three involve the familiar procedures of jeu de taquin, row insertion, and column insertion. The fourth operation, hopscotch, is new, although specialised versions have appeared previously. Like the other three operations, this new operation may be computed with a set of local rules in a growth diagram, and it preserves Knuth equivalence class. Each of these four operations gives rise to an a priori distinct theory of dual equivalence. We show that these four theories coincide. The four operations are linked via the involutive tableau operations of …