相关论文: Exotic symmetric space over a finite field, II

The goal of this article is twofold. First, we find a natural home for the double affine Hecke algebras (DAHA) in the physics of BPS states. Second, we introduce new invariants of torus knots and links called "hyperpolynomials" that address…

Intersection homology with coefficients in a field restores Poincar\'e duality for some spaces with singularities, as pseudomanifolds. But, with coefficients in a ring, the behaviours of manifolds and pseudomanifolds are different. This…

We construct an analogue of the Lyndon-Hochschild-Serre spectral sequence in the context of polynomial cohomology, for group extensions. If G is an extension of Q by H, then the spectral sequence converges to the polynomial cohomology of G.…

We study the exotic t-structure on the derived category of coherent sheaves on two-block Springer fibre (i.e. for a nilpotent matrix of type (m+n,n) in type A). The exotic t-structure has been defined by Bezrukavnikov and Mirkovic for…

In this paper, we mainly build up the theory of sheaf-correspondence filtered spaces and stratified de Rham complexes for studying singular spaces. We prove the finiteness of a stratified de Rham cohomology and obtain its isomorphism to…

We relate shuffle algebras, as defined by Nichols, Feigin-Odesskii and Rosso, to perverse sheaves on symmetric products of the complex line (i.e., on the spaces of monic polynomials stratified by multiplicities of roots). More precisely, we…

Contains a further development of the V.G. Maz'ya concept of polynomial capacities.A different different approach is given together with new results. The primary application is for Hardy inequalities. This is treated in a later report. Here…

The Hard Lefschetz theorem for intersection cohomology of nonrational polytopes was recently proved by K. Karu [Ka]. This theorem implies the conjecture of R. Stanley on the unimodularity of the generalized $h$-vector. In this paper we…

Motivated by the work of Koornwinder, Macdonald, Cherednik, Noumi, and van Diejen we define a 6-parameter double affine Hecke algebra and establish its basic structural properties, including the existence of an involution. We relate the…

In this paper, we obtain explicit expressions for Pandharipande-Pixton-Zvonkine relations in the second rational cohomology of $\overline{\mathcal{M}}_{g,n}$ and comparing the result with Arbarello-Cornalba's theorem we prove Pixton's…

Kato's exotic nilpotent cone was introduced as a substitute for the ordinary nilpotent cone of type C with cleaner properties. The geometric Robinson-Schensted correspondence is obtained by parametrizing the irreducible components of the…

We consider the topology for a class of hypersurfaces with highly nonisolated singularites which arise as exceptional orbit varieties of a special class of prehomogeneous vector spaces, which are representations of linear algebraic groups…

A classical Theorem of Alexandrov states that the map associating its boundary to a convex polyhdedron of the 3-dimensional Euclidean space is a bijection from the set of convex polyhdedron up to congruence to the set of isometry classes of…

In the present note we obtain new results on two conjectures by Csordas et al. regarding the interlacing property of zeros of special polynomials. These polynomials came from the Jacobi tau methods for the Sturm-Liouville eigenvalue…

The embedding of the isometry group of the coset spaces SU(1,n)/ U(1)xSU(n) in Sp(2n+2,R) is discussed. The knowledge of such embedding provides a tool for the determination of the holomorphic prepotential characterizing the special…

In this paper we define the coarse (co)homology of the complement of a subspace in a metric space, generalizing the coarse (co)homology of Roe. We give a model space which encodes coarse geometric structure of the complement. We also…

We explore connections between three structures associated with the cohomology of the moduli of 1-dimensional stable sheaves on $\mathbb{P}^2$: perverse filtrations, tautological classes, and refined BPS invariants for local $\mathbb{P}^2$.…

We show that, for a finite spectrum $X$, Spanier-Whitehead duality induces an isomorphism between the cohomological and homological Atiyah-Hirzebruch spectral sequences. As an application, it follows that Poincar\'e duality for a Poincar\'e…

This paper introduces some inverse sequences of different polyhedra all based on finite approximations of a compact metric space so they can be used to capture the shape type of the original space. It is shown that they are HPol-expansions,…

Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on R^2 are investigated under suitable continuity restrictions on cochains. The zeroth, first, and second cohomology spaces in…