相关论文: Stringy power operations in Tate K-theory

On a connected, oriented, smooth Riemannian manifold without boundary we consider a real scalar field whose dynamics is ruled by $E$, a second order elliptic partial differential operator of metric type. Using the functional formalism and…

We introduce a global equivariant refinement of algebraic K-theory; here `global equivariant' refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global…

For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of…

We describe how power operations descend through homotopy limit spectral sequences. We apply this to describe how norms appear in the $C_2$-equivariant Adams spectral sequence, to compute norms on $\pi_0$ of the equivariant $KU$-local…

Matthew Ando produced power operations in the Lubin-Tate cohomology theories and was able to classify which complex orientations were compatible with these operations. The methods used by Ando, Hopkins and Rezk to classify orientations of…

We construct string topology operations in twisted K-theory. We study the examples given by symplectic Grassmannians, computing the twisted K-theory of the loop spaces of quaternionic projective spaces in detail. Via the work of…

In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…

Using the Liu's method, we prove a new Witten rigidity theorem of elliptic genus of twisted Dirac operators in even dimensional spin manifolds under the circle action. Combined with the Han-Yu's method, we prove the Witten rigidity theorems…

Kitchloo and Morava give a strikingly simple picture of elliptic cohomology at the Tate curve by studying a completed version of $S^1$-equivariant $K$-theory for spaces. Several authors (cf [ABG],[KM],[L]) have suggested that an equivariant…

In this paper, we introduce the notion of $G_\infty$-ring spectra. These are globally equivariant homotopy types with a structured multiplication, giving rise to power operations on their equivariant homotopy and cohomology groups. We…

Given a topological group G, its orbit category Orb_G has the transitive G-spaces G/H as objects and the G-equivariant maps between them as morphisms. A well known theorem of Elmendorf then states that the category of G-spaces and the…

The ring of symmetric functions carries the structure of a Hopf algebra. When computing the coproduct of complete symmetric functions $h_\lambda$ one arrives at weighted sums over reverse plane partitions (RPP) involving binomial…

We realize a graded variant $K_0(Var_k^{dim})$ of the Grothendieck ring of varieties as a quadratic extension of the subring $K_0(Var_k^{sp})$ spanned by classes of smooth and proper varieties. As such, there exists a natural involution…

For closed and connected subgroups G of SO(n), we study the energy functional on the space of G-structures of a (compact) Riemannian manifold M, where G-structures are considered as sections of the quotient bundle O(M)/G. Then, we deduce…

Given a simple, simply connected compact Lie group G, let M be a G-space. We describe the quantization of the category of positive energy representations of the loop group of G at a given level and parametrized over the loop space LM. This…

Tangent spaces to Schubert varieties of type A were characterized by Lakshmibai and Seshadri. This result was extended to the other classical types by Lakshmibai. We give a uniform characterization of tangent spaces to Schubert varieties in…

The theory of quantum symmetric pairs is applied to $q$-special functions. Previous work shows the existence of a family $\chi$-spherical functions indexed by the integers for each Hermitian quantum symmetric pair. A distinguished family of…

This expository paper introduces several ideas in chromatic homotopy theory around Morava's extraordinary E-theories. In particular, we construct various moduli problems closely related to Lubin-Tate deformation theory and study their…

We use Grayson's binary multicomplex presentation of algebraic $K$-theory to give a new construction of exterior power operations on the higher $K$-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a…

In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl…