Related papers: Divided difference operators in equivariant $KK$-t…

In the present paper we provide a general algorithm to compute multiplicative cohomological operations on algebraic oriented cohomology of projective homogeneous G-varieties, where G is a split reductive algebraic group over a field of…

In a previous paper we introduced the unitary conjugation groupoid associated to any unital separable Type I C*-algebra. This groupoid encodes the representation-theoretic structure of the algebra through the action of its unitary group on…

Let $X$ be a complex scheme acted on by an affine algebraic group $G$. We prove that the Atiyah class of a $G$-equivariant perfect complex on $X$, as constructed by Huybrechts and Thomas, is $G$-equivariant in a precise sense. As an…

We consider a semi-classical completely integrable system defined by a $\hbar$-pseudodifferential operator $\hat{H}$ on the torus $\mathbb{T}^{d}$. In order to study perturbed operators of the form $\hat{H}+\hbar^{\kappa}\hat{K}$, where…

For a wide class of pairs of unbounded selfadjoint operators with bounded commutator we construct a K-theoretical integer invariant which is continuous, is equal to zero for commuting operators and is equal to one for the pair (x, i d/dx).

We construct families of bispectral difference operators of the form a(n)T + b(n) + c(n) T^{-1} where T is the shift operator. They are obtained as discrete Darboux transformations from appropriate extensions of Jacobi operators. We…

We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version…

A difference operator on an associative algebra is an algebraic abstraction of the forward and backward difference operators. In this paper, we first introduce difference operators on associative $2$-algebras and consider the category of…

If $G$ is a linearly reductive group acting rationally on a polynomial ring $S$, then the inclusion $S^{G} \hookrightarrow S$ possesses a unique $G$-equivariant splitting, called the Reynolds operator. We describe algorithms for computing…

Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For compact operators $T$, we give a complete…

Given an algebraic torus $T$ over a field $F$, its lattice of characters $\Lambda$ gives rise to a topological torus $\mathfrak{T}(T)=\Lambda_{\mathbb R}/\Lambda$ with a continuous action of the absolute Galois group $G$. We construct a…

We consider central simple $K$-algebras which happen to bedifferential graded $K$-algebras. Two such algebras $A$ and $B$are considered equivalent if there are bounded complexes of finite dimensional$K$-vector spaces $C_A$ and $C_B$ such…

For a compact simply connected simple Lie group $G$ with an involution $\alpha$, we compute the $G\rtimes \Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\Z/2$ acts either by $\alpha$ or by $g\mapsto \alpha(g)^{-1}$. We…

Using a global version of the equivariant Chern character, we describe the complexified twisted equivariant K-theory of a space with a compact Lie group action in terms of fixed-point data. We apply this to the case of a compact Lie group…

We prove a type-uniform Chevalley formula for multiplication with divisor classes in the equivariant quantum $K$-theory ring of any cominuscule flag variety $G/P$. We also prove that multiplication with divisor classes determines the…

We consider generalised Dirac--Schr\"odinger operators, consisting of a self-adjoint elliptic first-order differential operator D with a skew-adjoint 'potential' given by a (suitable) family of unbounded operators. The index of such an…

The goal of this paper is to construct a calculus whose higher indices are naturally elements in the twisted K-theory groups for Lie groupoids. Given a Lie groupoid $G$ and a $PU(H)$-valued groupoid cocycle, we construct an algebra of…

Let X be a T-variety, where T is an algebraic torus. We describe a fully faithful functor from the category of T-equivariant vector bundles on X to a certain category of filtered vector bundles on a suitable quotient of X by T. We show that…

The problem of a differential operator left- and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The…