1,721,014 research outputs found
A geometric realization of
No full textSummary: Given an orientable weakly self-dual manifold of rank two (see the second author, Asian J. Math. 9, No. 1, 79--101 (2005; Zbl 1085.14035)), we build a geometric realization of the Lie algebra \germ{sl}(6,\Bbb C) as a naturally defined algebra of endomorphisms of the space of differential forms of . We provide an explicit description of Serre generators in terms of natural generators of . This construction gives a bundle on which is related to the search for a natural gauge theory on . We consider this paper as a first step in the study of a rich and interesting algebraic structure
Symmetric group actions on the cohomology of configurations in R^d
No full textIn this paper we deal with the action of the symmetric group on the cohomology of the conguration space Cn(d) of n points in Rd. This topic has been studied by several authors and it is well-known that for d even H* (Cn(d);C) ≌ 2IndSnS21 while, for d odd, H* (Cn(d);C) ≌ CSn. On the cohomology algebra H* (Cn(d);C) there is, in addition to the natural Sn-action, an extended action of Sn+1; this was shown for the case when d is even by Mathieu, Robinson and Whitehouse and the second author using three dierent methods. For the case when d is odd it was shown by Mathieu (anyway we will give an elementary algebraic construction of the extended action for this case). The purpose of this article is to present some results that can be obtained, in an elementary way, exploiting the interplay between the extended action and the standard action. Among these we will recall a quick proof for the formula cited above for the case when d is even and show how to extend this proof to the case when d is odd. We will also show how to locate among the homogeneous components of the graded algebra H* (Cn(d);C) the copies of the standard, sign and standard tensor sign representations and we will give explicit formulas for both the extended and the canonical actions on the low-degree cohomology modules
Degrees of quantum function algebras at roots of 1
No full textAbstractIn this paper we will deal with quantum function algebrasFq[G] in the special case when the parameterqspecializes to a root of 1. Using a combinatorial technique, we will give general formulas for the degree of such algebras and of a particular family of quotients which are fundamental objects in representation theory
Models for real subspace arrangements and stratified manifolds
No full textWe consider a central subspace and half-space arrangement A in Euclidean vector space V, and let M(A) be its complement. We construct some compactifications for the C∞-manifold M(A)/R+. They turn out to be C∞-manifolds with corners whose boundary is determined by simple combinatorial data. This generalizes a construction described by Kontsevich in his paper on deformation quantization of Poisson manifolds. Then, we extend the construction to more general objects, that is, stratified real manifolds whose stratification locally looks like the one induced by an arrangement of linear (half-) spaces. The models we obtain are again C∞-manifolds with corners equipped with a nice combinatorial description of the boundary
Blow-ups and cohomology bases for De Concini - Procesi models of subspace arrangements
No full textIn this paper we are going to study the cohomology rings of De Concini–Procesi models (see [1]) of subspace arrangements
Wonderful models of the braid arrangements (contributo in atti di seminario, Young Algebra Seminar, Universita' di Tor Vergata).
No full textYoung Algebra Seminar, Universita' di Tor Vergata
The actions of S_{n+1} and S_{n} on the cohomology ring of a Coxeter arrangement of type A_{n-1}
No full textExponential formulas for models of complex reflection groups
Full text linkIn this paper we find exponential formulas for the Betti numbers of the De Concini-Procesi minimal wonderful models YG(r,p,n) associated to the complex reflection groups G(r, p, n). Our formulas are different from the ones already known in the literature: they are obtained by a new combinatorial encoding of the elements of a basis of the cohomology by means of set partitions with weights and exponents.We also point out that a similar combinatorial encoding can be used to describe the faces of the real spherical wonderful models of type An-1(=G(1, 1, n)), Bn (=G(2, 1, n)) and Dn(=G(2, 2, n)). This provides exponential formulas for the f-vectors of the associated nestohedra: the Stasheff's associahedra (in this case closed formulas are well known) and the graph associahedra of type Dn
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