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Invariant vectors and level raising operators in representations of the p-adic group GL(3)
(2012)
Each irreducibel, admissible representation (&pi,V) of GL(n) over a non-archimedean local field F has associated fixed vector spaces VK(m), for K(m) a compact-open subgroup of GL(n). It is known that there exists some ...
Symmetric Tensors and Combinatorics for Finite-Dimensional Representations of Symplectic Lie Algebras
(2012)
First, we develop a result using multilinear algebra to prove, in an elementary way, a useful identity between representations of $\mathfrak{sp}(4, \mathbb{C})$, which involves writing any irreducible representation as a ...
A Guided Reinvention of Ring, Integral Domain, and Field
(2012)
Abstract algebra enjoys a prestigious position in mathematics and the undergraduate mathematics curriculum. A typical abstract algebra course aims to provide students with a glimpse into the elegance of mathematics by ...
SELF-DUAL REPRESENTATIONS WITH VECTORS FIXED UNDER AN IWAHORI SUBGROUP
(2012)
Let $G$ be the group of $F$-points of a split connected reductive $F$-group over a non-Archimedean local field $F$ of characteristic 0. Let $\pi$ be an irreducible smooth self-dual representation of $G$. The space $W$ of ...
Comparison Theorems, Geomatric Inequalities, And Applications to p-harmonic Geometry
(2012)
In this dissertation, we consider three aspects: comparison theorems on complete manifold which posses a pole, geometric inequalities on complete manifolds, and the applications of inequalities to p-harmonic geometry. More ...
Comparison Theorems, Geomatric Inequalities, And Applications to p-harmonic Geometry
(2012)
In this dissertation, we consider three aspects: comparison theorems on complete manifold which posses a pole, geometric inequalities on complete manifolds, and the applications of inequalities to p-harmonic geometry. More ...
Optimization Problem for Klein-Gordon Equation
(2012)
We consider a damped Klein-Gordon equation with a variable diffusion coefficient. The goal is to derive necessary conditions for the optimal set of parameters minimizing the objective function J. First, we show that the ...
MATHEMATICAL THEORY IN CLASSIFICATION AND SEGMENTATION
(2012)
We develop several mathematical approaches to solve a series of questions of interdisciplinary research interests. New distance functions are designed for the verification of meteorological forecasts. Modern active contour ...
Geometry of Houghton's Groups
(2012)
Ken Brown showed finiteness properties of Houghton's groups by studying the action of those groups on infinite dimensional cell complex. We modify his proof by construction finite dimensional CAT(0) cubical complexes on ...