On extended umbral calculus, oscillator-like algebras and Generalized Clifford Algebra

Formal calculus and umbral calculus

In this paper we use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus and we introduce and study certain operators generalizing the classical umbral shifts. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a short, elementary proof which naturally arose as a motivating computation related to a certain crucial "associativity" property of an important class of vertex operator algebras. Very similar (somewhat forgotten) proofs had appeared…

On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices

Based on \cite{DH94}, we introduce a bijective correspondence between first order differential calculi and the graph structure of the symmetric lattice that allows one to encode completely the interconnection structure of the graph in the exterior derivative. As a result, we obtain the Grassmannian character of the lattice as well as the mutual commutativity between basic vector-fields on the tangent space. This in turn gives several similarities between the Clifford setting and the algebra of endomorphisms endowed by the graph structure, such as the hermitian structure of the lattice as well …

通过Clifford代数的Grassmannian等变量子上同调

Equivariant Quantum Cohomology of Grassmannians via the Clifford algebra

本文通过构造显式的等变量子Satake映射，将Grassmannian的环面等变量子上同调表示为射影空间的等变量子上同调，并利用Clifford代数结构导出等变Gromov-Witten不变量的新递推关系，从而给出其基于Wick定理的计算方法，并应用于证明等变量子Pieri规则的Graham正性。