Related papers: Branching Rules For Splint Root Systems

We consider a complex version of the $\vee$-systems, which appeared in the theory of the WDVV equation. We show that the class of these systems is closed under the natural operations of restriction and taking the subsystems and study a…

Explicit expressions are presented for general branching functions for cosets of affine Lie algebras $\hat{g}$ with respect to subalgebras $\hat{g}^\prime$ for the cases where the corresponding finite dimensional algebras $g$ and $g^\prime$…

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…

We study the double slice genus of a knot, a natural generalization of slice genus. We define a notion called band number, a natural generalization of band unknotting number, and prove it is an upper bound on double slice genus. Our bound…

We prove a prime decomposition theorem for string links in a thickened surface. Namely, we prove that any non-braid string link $\ell \subset \Sigma \times I$, where $\Sigma$ is a compact orientable (not necessarily closed) surface other…

We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…

We give a branching law for subgroups fixed by an involution. As an application we give a generalization of the Cartan-Helgason theorem and a noncompact analogue of the Borel-Weil theorem.

Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also called subdivision symbols, which describe the linear rules…

We construct parametric families of (monic) reducible polynomials having two roots very close to each other.

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…

In this paper we propose a novel efficient algorithm for calculating winding numbers, aiming at counting the number of roots of a given polynomial in a convex region on the complex plane. This algorithm can be used for counting and…

Given any polynomial system with fixed monomial term structure, we give explicit formulae for the generic number of roots with specified coordinate vanishing restrictions. For the case of affine space minus an arbitrary union of coordinate…

Third-order ordinary differential equations with Lie symmetry algebras isomorphic to the nonsolvable algebra $\mathfrak{sl}(2,\mathbb{R})$ admit solvable structures. These solvable structures can be constructed by using the basis elements…

This is a long introduction to the theory of "branch groups": groups acting on rooted trees which exhibit some self-similarity features in their lattice of subgroups.

The initial classification of fusion rules have shown that rational conformal field theory is very limited. In this paper we study the fusion rules of extend ed current algebras. Explicit formulas are given for the S matrix and the fusion…

Given a class of objects, a pattern theorem is a powerful result describing their structure. We show that alternating knots exhibit a pattern theorem, and use this result to prove a long-standing conjecture that alternating knots grow rare.…

The goal of this paper has two-folds. First, we establish skeleton and spine decompositions for superprocesses whose underlying processes are general symmetric Hunt processes. Second, we use these decompositions to obtain weak and strong…

We try to write (generic) elements of classical simple Lie algebras as sums of as few elements of the orbit C of long root vectors as possible. If the Lie algebra in question is sl_n or sp_n, then C consists of all rank 1 matrices in the…

The natural numbers divisible by the Prime Factors 2, 3, 5, 11, 13 and 17 lie on defined spiral graphs, which run through the Square Root Spiral. A mathematical analysis shows, that these spiral graphs are defined by specific quadratic…

We introduce a class of graphs with coloured edges to encode subsystems of the classical root systems, which in particular classify them up to equivalence. We further use the graphs to describe root-kernel intersections, as well as…