Related papers: On the combinatorics of string polytopes

This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…

We show that string algebras are `homologically tame' in the following sense: First, the syzygies of arbitrary representations of a finite dimensional string algebra $\Lambda$ are direct sums of cyclic representations, and the left…

Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid $M$. Our main result is that these polynomials are determined by Betti numbers associated with graded…

We show that for any permutation $w$ that avoids a certain set of 13 patterns of lengths 5 and 6, the Schubert polynomial $\mathfrak S_w$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner…

We show that the central charges that group theory allows in the (2,0) supersymmetry translations algebra arise from a string and a 3-brane by commuting two supercharges. We show that the net force between two such parallel strings…

Suppose that $\mathbf{C}_0^n \subset \mathbb{R}^{n+1}$ is a smooth strictly minimizing and strictly stable minimal hypercone, $l \geq 0$, and $M$ a complete embedded minimal hypersurface of $\mathbb{R}^{n+1+l}$ lying to one side of…

The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra. In this article, we consider a modular version of the theory, and show that…

We return to and refine Zwiebach's formulation of closed string field theory (CSFT) built around non-critical backgrounds [1,2], restricting our attention to genus zero. The structure involves a special string state $F$ that encodes the…

We present a class of static, spherically symmetric, non-singular solutions of the tree-level string effective action, truncated to first order in $\alpha'$. In the string frame the solutions approach asymptotically (at $r\to 0$ and $r\to…

Let Phi be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Phi is a Dirichlet series in r complex variables s_1,...,s_r, initially converging for Re(s_i) sufficiently large, that has meromorphic continuation to…

Let $\mathcal{O}(\mbox{Spin}_{q^{1/2}}(2n+1))$ and $\mathcal{O}(SO_q(2n+1))$ be the quantized algebras of regular functions on the Lie groups $\mbox{Spin}(2n+1)$ and $SO(2n+1)$, respectively. In this article, we prove that the…

The heterotic string occurs as a soliton of the type I superstring in ten dimensions, supporting the conjecture that these two theories are equivalent. The conjecture that the type IIB string is self-dual, with the strong coupling dynamics…

When $\lambda$ is a partition, the specialized non-symmetric Macdonald polynomial $E_{\lambda}(x;q;0)$ is symmetric and related to a modified Hall--Littlewood polynomial. We show that whenever all parts of the integer partition $\lambda$ is…

We consider Drinfeld-Sokolov bihamiltonian structure associated to a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On this space, we construct a local…

We study different phenomenological aspects of compact, D=4, N=1 Type IIB orientifolds considered as models for unification of the standard model and gravity. We discuss the structure of the compactification, string and unification scales…

This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string…

Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of…

We provide a complete classification of Clifford quantum cellular automata (QCAs) on arbitrary metric spaces and any qudits (of prime or composite dimensions) in terms of algebraic L-theory. Building on the delooping formalism of Pedersen…

Kostant asked the following question: Let $\mathfrak{g}$ be a simple Lie algebra over the complex numbers. Let $\lambda$ be a dominant integral weight. Then, $V(\lambda)$ is a component of $V(\rho)\otimes V(\rho)$ if and only if $\lambda…

Let w be an elliptic element of the Weyl group of a connected reductive group G. Let X be the set of pairs (g,B) where g is an element of G, B is a Borel subgroup of G and B,gBg^{-1} are in relative position w. Then G acts naturally on X.…