Let G denote a connected reductive group over a nonarchimedean local field F . Let K denote a special maximal parahoric subgroup of G(F ). We establish a Satake isomorphism for the Hecke algebra HK of K-bi-invariant compactly supported functions on G(F ). The key ingredient is a Cartan decomposition describing the double coset space K\G(F )/K. We also describe how our results relate to the trea...

A normal projective variety X is called Fano if a multiple of the anticanonical Weil divisor, −KX , is an ample Cartier divisor. The importance of Fano varieties is twofold, from one side they give, has predicted by Fano [Fa], examples of non rational varieties having plurigenera and irregularity all zero (cfr [Is]); on the other hand they should be the building block of uniruled variety. Indee...

We introduce a notion of morphism of CohFT algebras, based on the analogy with A∞ morphisms. We outline the construction of a “quantization” of the classical Kirwan morphism to a morphism of CohFT algebras from the equivariant quantum cohomology of a Gvariety to the quantum cohomology of its geometric invariant theory or symplectic quotient, and an example relating to the orbifold quantum cohom...

We construct an intersection product on tropical cycles contained in the Bergman fan of a matroid. To do this we first establish a connection between the operations of deletion and restriction in matroid theory and tropical modifications as defined by Mikhalkin in [14]. This product generalises the product of Allermann and Rau [2], and Allermann [1] and also provides an alternative procedure fo...

The Harish-Chandra homomorphism is due to [Harish-Chandra 1951]. Attention to universal modules with highest weights is in ]Harish-Chandra 1951], [Cartier 1955], as well as [Verma 1968], [BernsteinGelfand-Gelfand 1971a], [Bernstein-Gelfand-Gelfand 1971b], [Bernstein-Gelfand-Gelfand 1975]. See also [Jantzen 1979]. [1] We treat sl(2) in as simple a style as possible, to highlight ideas. Then sl(3...

MCDONALD and MCDONALD [1] present a version of the history of mesothelioma that for the sake of scholarship requires amendment. The references to the growth of knowledge of an association between mesothelioma and asbestos exposure are at variance with plain reading of the publications they cited. For example, GLOYNE [2] stated that he considered it worthwhile recording his two cases of squamous...

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

We prove an analogue of the Poincaré-Birkhoff-Witt theorem and of the Cartier-Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a B∞-algebra. We construct a universal enveloping functor U2 from B∞-algebras to 2-associative algebras, i.e. algebras equipped with two associative operations. We show that any cofree Hopf algebra H is of the form...

Let (X0, B0) be the canonical limit of a one-parameter family of stable pairs, provided by the log Minimal Model Program. We prove that X0 is S2 and that ⌊B0⌋ is S1, as an application of a general local statement: if (X,B+ ǫD) is log canonical and D is Q-Cartier then D is S2 and ⌊B⌋ ∩D is S1, i.e. has no embedded components. When B has coefficients < 1, examples due to Hacking and Hassett show ...

Noises: a nonstandard analysis. Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y. Perrin, an appropriate mathematical framework is derived for new non-asymptotic estimation techniques, which do not necessitate any statistical analysis of the noises corrupting any sensor. Various applications are deduced for multiplicative noises, for the length of t...