Related papers: Atiyah class and Chern character for global matrix…

We present combinatorial/geometric obstructions induced by the factorization over the integers of the Chern polynomial of the bundle of logarithmic vector fields associated to a complex projective plane curve. Our results generalize at the…

The $L^2$-Index Theorem of Atiyah \cite{atiyah} expresses the index of an elliptic operator on a closed manifold $M$ in terms of the $G$-equivariant index of some regular covering $\widetilde{M}$ of $M$, with $G$ the group of covering…

We propose a specific class of matrices which participate in factorization problems that turn to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang-Baxter maps, expressed in non-commutative variables.…

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

Costello and Gwilliam have given both 1) a general definition of perturbative quantum gauge theory on a manifold M and 2) a construction of a factorization algebra of quantum observables assigned to every quantum gauge theory. In this…

We prove two geometric index theorems for a family of first-order elliptic operators over a manifold with boundary by computing eta form representatives for the Chern character classes of the index bundle. The eta forms occur as relative…

Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…

This paper consists of three components. In the first, we give an adelic interpretation of the classical extension class associated to extension of locally free sheaves on curves. Then, in the second, we use this construction on adelic…

In recent papers and books, a global quantization has been developed for unimodular groups of type I. It involves operator-valued symbols defined on the product between the group $\mathsf{G}$ and its unitary dual $\widehat{\mathsf{G}}$,…

In this paper we prove a characterization of quotients of Abelian varieties by the actions of finite groups that are free in codimension-one via some vanishing conditions on the orbifold Chern classes. The characterization is given among a…

This article generalizes the correspondence between matrix factorizations and maximal Cohen-Macaulay modules over hypersurface rings due to Eisenbud and Yoshino. We consider factorizations with several factors in a purely categorical…

For a fixed integer $t \geq 2$, we consider the irreducible characters of representations of the classical groups of types A, B, C and D, namely $\text{GL}_{tn}, \text{SO}_{2tn+1}, \text{Sp}_{2tn}$ and $\text{O}_{2tn}$, evaluated at…

In this paper we present the most complete description as possible of the factorization of the general polar of the general member of an equisingularity class of irreducible germs of complex plane curves. Our result will refine the rough…

We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed.…

In our previous paper math.QA/0412192 the Cayley-Hamilton identity for the GL(m|n) type quantum matrix algebra was obtained. Here we continue investigation of that identity. We derive it in three alternative forms and, most importantly, we…

We describe a generalization of the usual boundary strata classes in the Chow ring of $\overline{\mathcal{M}}_{g,n}$. The generalized boundary strata classes additively span a subring of the tautological ring. We describe a multiplication…

We study the ring of characteristic classes with values in the Chow ring for principal $G$-bundles over schemes. If we consider bundles which are locally trivial in the Zariski topology, then we show, for $G$ reductive, that this ring is…

The so-called multilayer wave functions were introduced in the study of the fractional Quantum Hall effect by Halperin and others. They are defined with the help of a symmetric matrix $K$ in $M^k(\mathbb{N})$, which encodes the couplings…

Let $d$ be a positive integer. The Yangian $Y_d=Y(\mathfrak{gl}(d,\mathbb C))$ of the general linear Lie algebra $\mathfrak{gl}(d,\mathbb C)$ has countably many generators and quadratic-linear defining relations, which can be packed into a…

This paper is a continuation of [GLT], which develops a level theory and establishes strong character bounds for finite simple groups of linear and unitary type in the case that the centralizer of the element has small order compared to…