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C. De Concini

Publications and source records attributed to C. De Concini.

9 recordsLinked to original sources
arXiv2012

Box splines and the equivariant index theorem

In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of G in a vector space M can be both described using some vector spaces of distributions, on the dual of the group G or on the dual of its Lie algebra. The morphism from K-theory to cohomology is analyzed and the multiplication by the Todd class is shown to correspond to the operator (deconvolution) inverting the semidiscrete convolution with a box spline. Finally, the multiplicities of the index of a G-transversally elliptic operator on M are determined using the infinitesimal index of the symbol.

math.DG↗
arXiv2008

Vector partition function and generalized Dahmen-Micchelli spaces

This is the first of two papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index theory will appear in a subsequent paper.

math.CO↗
arXiv2006

The algebra of the box spline

In this paper we want to revisit results of Dahmen and Micchelli on box-splines which we reinterpret and make more precise. We compare these ideas with the work of Brion, Szenes, Vergne and others on polytopes and partition functions.

math.NA↗
arXiv2005

On the geometry of toric arrangements

We introduce toric arrangements, essentially finite families of codimension 1 subtori of a torus or of their cosets, as a periodic generalization of hyperplane arrangements, compute cohomology of the complement of such an arrangement and apply the theory to give a geometric interpretation of the formulas of Brion--Szenes--Vergne counting the number of integral points in polytopes.

math.AG↗
arXiv2004

On the geometry of graph arrangements

We use the results of AG/0406290 to discuss the counting formulas of network flow polytopes and magic squares, i.e. the formula for the corresponding Ehrhart polynomial in terms of residues. We also discuss a description of the big cells using the theory of non broken circuit bases.

math.CO↗
arXiv2003

Nesting maps of Grassmannians

Let F be a field and i < j be integers between 1 and n. A map of Grassmannians f : Gr(i, F^n) --> Gr(j, F^n) is called nesting, if l is contained in f(l) for every l in Gr(i, F^n). We show that there are no continuous nesting maps over C and no algebraic nesting maps over any algebraically closed field F, except for a few obvious ones. The continuous case is due to Stong and Grover-Homer-Stong; the algebraic case in characteristic zero can also be deduced from their results. In this paper we give new proofs that work in arbitrary characteristic. As a corollary, we give a description of the algebraic subbundles of the tangent bundle to the projective space P^n over F. Another application can be found in a recent paper math.AC/0306126 of George Bergman.

math.AG↗
arXiv1998

On the work of Givental relative to mirror symmetry

These are the informal notes of two seminars held at the Universita` di Roma "La Sapienza", and at the Scuola Normale Superiore in Pisa in Spring and Autumn 1997. We discuss in detail the content of the parts of Givental's paper dealing with mirror symmetry for projective complete intersections.

math.AG↗
arXiv1993

Some quantum analogues of solvable Lie groups

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras of twisted polynomials with a derivation, an object which has often appeared in the general theory of non-commutative rings. In particular, we find maximal dimensions of their irreducible representations. Our results confirm the validity of the general philosophy that the representation theory is intimately connected to the Poisson geometry.

hep-th↗