Displaying similar documents to “Hecke operators on the q -analogue of group cohomology.”

Twisted action of the symmetric group on the cohomology of a flag manifold

Alain Lascoux, Bernard Leclerc, Jean-Yves Thibon (1996)

Banach Center Publications

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Classes dual to Schubert cycles constitute a basis on the cohomology ring of the flag manifold F, self-adjoint up to indexation with respect to the intersection form. Here, we study the bilinear form (X,Y) :=〈X·Y, c(F)〉 where X,Y are cocycles, c(F) is the total Chern class of F and〈,〉 is the intersection form. This form is related to a twisted action of the symmetric group of the cohomology ring, and to the degenerate affine Hecke algebra. We give a distinguished basis for this form,...

CM liftings of supersingular elliptic curves

Ben Kane (2009)

Journal de Théorie des Nombres de Bordeaux

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Assuming GRH, we present an algorithm which inputs a prime p and outputs the set of fundamental discriminants D < 0 such that the reduction map modulo a prime above p from elliptic curves with CM by 𝒪 D to supersingular elliptic curves in characteristic p is surjective. In the algorithm we first determine an explicit constant D p so that | D | > D p implies that the map is necessarily surjective and then we compute explicitly the cases | D | < D p .

On the real cohomology of spaces of free loops on manifolds

Katsuhiko Kuribayashi (1996)

Fundamenta Mathematicae

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Let LX be the space of free loops on a simply connected manifold X. When the real cohomology of X is a tensor product of algebras generated by a single element, we determine the algebra structure of the real cohomology of LX by using the cyclic bar complex of the de Rham complex Ω(X) of X. In consequence, the algebra generators of the real cohomology of LX can be represented by differential forms on LX through Chen’s iterated integral map. Let 𝕋 be the circle group. The 𝕋 -equivariant...

Certain L-functions at s = 1/2

Shin-ichiro Mizumoto (1999)

Acta Arithmetica

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Introduction. The vanishing orders of L-functions at the centers of their functional equations are interesting objects to study as one sees, for example, from the Birch-Swinnerton-Dyer conjecture on the Hasse-Weil L-functions associated with elliptic curves over number fields.    In this paper we study the central zeros of the following types of L-functions:    (i) the derivatives of the Mellin transforms of Hecke eigenforms for SL₂(ℤ),    (ii)...

The cohomology algebra of certain free loop spaces

Toshihiro Yamaguchi, Katsuhiko Kuribayashi (1997)

Fundamenta Mathematicae

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Let X be a simply connected space and LX the space of free loops on X. We determine the mod p cohomology algebra of LX when the mod p cohomology of X is generated by one element or is an exterior algebra on two generators. We also provide lower bounds on the dimensions of the Hodge decomposition factors of the rational cohomology of LX when the rational cohomology of X is a graded complete intersection algebra. The key to both of these results is the identification of an important subalgebra...

On the homotopy category of Moore spaces and the cohomology of the category of abelian groups

Hans-Joachim Baues, Manfred Hartl (1996)

Fundamenta Mathematicae

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The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James-Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space.